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multistep</title> <meta name="description" content="Search results for: linear multistep"> <meta name="keywords" content="linear multistep"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none 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action="https://publications.waset.org/abstracts/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="linear multistep"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 3374</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: linear multistep</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3374</span> Starting Order Eight Method Accurately for the Solution of First Order Initial Value Problems of Ordinary Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=James%20Adewale">James Adewale</a>, <a href="https://publications.waset.org/abstracts/search?q=Joshua%20Sunday"> Joshua Sunday</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we developed a linear multistep method, which is implemented in predictor corrector-method. The corrector is developed by method of collocation and interpretation of power series approximate solutions at some selected grid points, to give a continuous linear multistep method, which is evaluated at some selected grid points to give a discrete linear multistep method. The predictors were also developed by method of collocation and interpolation of power series approximate solution, to give a continuous linear multistep method. The continuous linear multistep method is then solved for the independent solution to give a continuous block formula, which is evaluated at some selected grid point to give discrete block method. Basic properties of the corrector were investigated and found to be zero stable, consistent and convergent. The efficiency of the method was tested on some linear, non-learn, oscillatory and stiff problems of first order, initial value problems of ordinary differential equations. The results were found to be better in terms of computer time and error bound when compared with the existing methods. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=predictor" title="predictor">predictor</a>, <a href="https://publications.waset.org/abstracts/search?q=corrector" title=" corrector"> corrector</a>, <a href="https://publications.waset.org/abstracts/search?q=collocation" title=" collocation"> collocation</a>, <a href="https://publications.waset.org/abstracts/search?q=interpolation" title=" interpolation"> interpolation</a>, <a href="https://publications.waset.org/abstracts/search?q=approximate%20solution" title=" approximate solution"> approximate solution</a>, <a href="https://publications.waset.org/abstracts/search?q=independent%20solution" title=" independent solution"> independent solution</a>, <a href="https://publications.waset.org/abstracts/search?q=zero%20stable" title=" zero stable"> zero stable</a>, <a href="https://publications.waset.org/abstracts/search?q=consistent" title=" consistent"> consistent</a>, <a href="https://publications.waset.org/abstracts/search?q=convergent" title=" convergent"> convergent</a> </p> <a href="https://publications.waset.org/abstracts/17775/starting-order-eight-method-accurately-for-the-solution-of-first-order-initial-value-problems-of-ordinary-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/17775.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">501</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3373</span> Constant Order Predictor Corrector Method for the Solution of Modeled Problems of First Order IVPs of ODEs</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20A.%20James">A. A. James</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20O.%20Adesanya"> A. O. Adesanya</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20R.%20Odekunle"> M. R. Odekunle</a>, <a href="https://publications.waset.org/abstracts/search?q=D.%20G.%20Yakubu"> D. G. Yakubu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=interpolation" title="interpolation">interpolation</a>, <a href="https://publications.waset.org/abstracts/search?q=approximate%20solution" title=" approximate solution"> approximate solution</a>, <a href="https://publications.waset.org/abstracts/search?q=collocation" title=" collocation"> collocation</a>, <a href="https://publications.waset.org/abstracts/search?q=differential%20system" title=" differential system"> differential system</a>, <a href="https://publications.waset.org/abstracts/search?q=half%20step" title=" half step"> half step</a>, <a href="https://publications.waset.org/abstracts/search?q=converges" title=" converges"> converges</a>, <a href="https://publications.waset.org/abstracts/search?q=block%20method" title=" block method"> block method</a>, <a href="https://publications.waset.org/abstracts/search?q=efficiency" title=" efficiency"> efficiency</a> </p> <a href="https://publications.waset.org/abstracts/1645/constant-order-predictor-corrector-method-for-the-solution-of-modeled-problems-of-first-order-ivps-of-odes" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/1645.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">337</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3372</span> A Continuous Boundary Value Method of Order 8 for Solving the General Second Order Multipoint Boundary Value Problems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=T.%20A.%20Biala">T. A. Biala</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper deals with the numerical integration of the general second order multipoint boundary value problems. This has been achieved by the development of a continuous linear multistep method (LMM). The continuous LMM is used to construct a main discrete method to be used with some initial and final methods (also obtained from the continuous LMM) so that they form a discrete analogue of the continuous second order boundary value problems. These methods are used as boundary value methods and adapted to cope with the integration of the general second order multipoint boundary value problems. The convergence, the use and the region of absolute stability of the methods are discussed. Several numerical examples are implemented to elucidate our solution process. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=linear%20multistep%20methods" title="linear multistep methods">linear multistep methods</a>, <a href="https://publications.waset.org/abstracts/search?q=boundary%20value%20methods" title=" boundary value methods"> boundary value methods</a>, <a href="https://publications.waset.org/abstracts/search?q=second%20order%20multipoint%20boundary%20value%20problems" title=" second order multipoint boundary value problems"> second order multipoint boundary value problems</a>, <a href="https://publications.waset.org/abstracts/search?q=convergence" title=" convergence"> convergence</a> </p> <a href="https://publications.waset.org/abstracts/50749/a-continuous-boundary-value-method-of-order-8-for-solving-the-general-second-order-multipoint-boundary-value-problems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/50749.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">377</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3371</span> On a Continuous Formulation of Block Method for Solving First Order Ordinary Differential Equations (ODEs)</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20M.%20Sagir">A. M. Sagir</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The aim of this paper is to investigate the performance of the developed linear multistep block method for solving first order initial value problem of Ordinary Differential Equations (ODEs). The method calculates the numerical solution at three points simultaneously and produces three new equally spaced solution values within a block. The continuous formulations enable us to differentiate and evaluate at some selected points to obtain three discrete schemes, which were used in block form for parallel or sequential solutions of the problems. A stability analysis and efficiency of the block method are tested on ordinary differential equations involving practical applications, and the results obtained compared favorably with the exact solution. Furthermore, comparison of error analysis has been developed with the help of computer software. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=block%20method" title="block method">block method</a>, <a href="https://publications.waset.org/abstracts/search?q=first%20order%20ordinary%20differential%20equations" title=" first order ordinary differential equations"> first order ordinary differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20multistep" title=" linear multistep"> linear multistep</a>, <a href="https://publications.waset.org/abstracts/search?q=self-starting" title=" self-starting"> self-starting</a> </p> <a href="https://publications.waset.org/abstracts/3622/on-a-continuous-formulation-of-block-method-for-solving-first-order-ordinary-differential-equations-odes" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/3622.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">306</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3370</span> Basis Theorem of Equivalence of Explicit-Type Iterations for the Class of Multivalued Phi-Quasi-Contrative Maps in Modular Function Spaces</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hudson%20Akewe">Hudson Akewe</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We prove that the convergence of explicit Mann, explicit Ishikawa, explicit Noor, explicit SP, explicit multistep and explicit multistep-SP fixed point iterative procedures are equivalent for the classes of multi-valued phi-contraction, phi-Zamfirescu and phi-quasi-contractive mappings in the framework of modular function spaces. Our results complement equivalence results on normed and metric spaces in the literature as they elegantly cut out the triangle inequality. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=multistep%20iterative%20procedures" title="multistep iterative procedures">multistep iterative procedures</a>, <a href="https://publications.waset.org/abstracts/search?q=multivalued%20mappings" title=" multivalued mappings"> multivalued mappings</a>, <a href="https://publications.waset.org/abstracts/search?q=equivalence%20results" title=" equivalence results"> equivalence results</a>, <a href="https://publications.waset.org/abstracts/search?q=fixed%20point" title=" fixed point"> fixed point</a> </p> <a href="https://publications.waset.org/abstracts/148112/basis-theorem-of-equivalence-of-explicit-type-iterations-for-the-class-of-multivalued-phi-quasi-contrative-maps-in-modular-function-spaces" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/148112.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">132</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3369</span> A Hybrid Block Multistep Method for Direct Numerical Integration of Fourth Order Initial Value Problems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Adamu%20S.%20Salawu">Adamu S. Salawu</a>, <a href="https://publications.waset.org/abstracts/search?q=Ibrahim%20O.%20Isah"> Ibrahim O. Isah</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Direct solution to several forms of fourth-order ordinary differential equations is not easily obtained without first reducing them to a system of first-order equations. Thus, numerical methods are being developed with the underlying techniques in the literature, which seeks to approximate some classes of fourth-order initial value problems with admissible error bounds. Multistep methods present a great advantage of the ease of implementation but with a setback of several functions evaluation for every stage of implementation. However, hybrid methods conventionally show a slightly higher order of truncation for any k-step linear multistep method, with the possibility of obtaining solutions at off mesh points within the interval of solution. In the light of the foregoing, we propose the continuous form of a hybrid multistep method with Chebyshev polynomial as a basis function for the numerical integration of fourth-order initial value problems of ordinary differential equations. The basis function is interpolated and collocated at some points on the interval [0, 2] to yield a system of equations, which is solved to obtain the unknowns of the approximating polynomial. The continuous form obtained, its first and second derivatives are evaluated at carefully chosen points to obtain the proposed block method needed to directly approximate fourth-order initial value problems. The method is analyzed for convergence. Implementation of the method is done by conducting numerical experiments on some test problems. The outcome of the implementation of the method suggests that the method performs well on problems with oscillatory or trigonometric terms since the approximations at several points on the solution domain did not deviate too far from the theoretical solutions. The method also shows better performance compared with an existing hybrid method when implemented on a larger interval of solution. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chebyshev%20polynomial" title="Chebyshev polynomial">Chebyshev polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=collocation" title=" collocation"> collocation</a>, <a href="https://publications.waset.org/abstracts/search?q=hybrid%20multistep%20method" title=" hybrid multistep method"> hybrid multistep method</a>, <a href="https://publications.waset.org/abstracts/search?q=initial%20value%20problems" title=" initial value problems"> initial value problems</a>, <a href="https://publications.waset.org/abstracts/search?q=interpolation" title=" interpolation"> interpolation</a> </p> <a href="https://publications.waset.org/abstracts/113723/a-hybrid-block-multistep-method-for-direct-numerical-integration-of-fourth-order-initial-value-problems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/113723.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">122</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3368</span> High Order Block Implicit Multi-Step (Hobim) Methods for the Solution of Stiff Ordinary Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=J.%20P.%20Chollom">J. P. Chollom</a>, <a href="https://publications.waset.org/abstracts/search?q=G.%20M.%20Kumleng"> G. M. Kumleng</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Longwap"> S. Longwap</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The search for higher order A-stable linear multi-step methods has been the interest of many numerical analysts and has been realized through either higher derivatives of the solution or by inserting additional off step points, supper future points and the likes. These methods are suitable for the solution of stiff differential equations which exhibit characteristics that place a severe restriction on the choice of step size. It becomes necessary that only methods with large regions of absolute stability remain suitable for such equations. In this paper, high order block implicit multi-step methods of the hybrid form up to order twelve have been constructed using the multi-step collocation approach by inserting one or more off step points in the multi-step method. The accuracy and stability properties of the new methods are investigated and are shown to yield A-stable methods, a property desirable of methods suitable for the solution of stiff ODE’s. The new High Order Block Implicit Multistep methods used as block integrators are tested on stiff differential systems and the results reveal that the new methods are efficient and compete favourably with the state of the art Matlab ode23 code. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=block%20linear%20multistep%20methods" title="block linear multistep methods">block linear multistep methods</a>, <a href="https://publications.waset.org/abstracts/search?q=high%20order" title=" high order"> high order</a>, <a href="https://publications.waset.org/abstracts/search?q=implicit" title=" implicit"> implicit</a>, <a href="https://publications.waset.org/abstracts/search?q=stiff%20differential%20equations" title=" stiff differential equations"> stiff differential equations</a> </p> <a href="https://publications.waset.org/abstracts/5700/high-order-block-implicit-multi-step-hobim-methods-for-the-solution-of-stiff-ordinary-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/5700.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">358</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3367</span> Development of Variable Order Block Multistep Method for Solving Ordinary Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohamed%20Suleiman">Mohamed Suleiman</a>, <a href="https://publications.waset.org/abstracts/search?q=Zarina%20Bibi%20Ibrahim"> Zarina Bibi Ibrahim</a>, <a href="https://publications.waset.org/abstracts/search?q=Nor%20Ain%20Azeany"> Nor Ain Azeany</a>, <a href="https://publications.waset.org/abstracts/search?q=Khairil%20Iskandar%20Othman"> Khairil Iskandar Othman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a class of variable order fully implicit multistep Block Backward Differentiation Formulas (VOBBDF) using uniform step size for the numerical solution of stiff ordinary differential equations (ODEs) is developed. The code will combine three multistep block methods of order four, five and six. The order selection is based on approximation of the local errors with specific tolerance. These methods are constructed to produce two approximate solutions simultaneously at each iteration in order to further increase the efficiency. The proposed VOBBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with single order Block Backward Differentiation Formula (BBDF). Numerical results shows the advantage of using VOBBDF for solving ODEs. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=block%20backward%20differentiation%20formulas" title="block backward differentiation formulas">block backward differentiation formulas</a>, <a href="https://publications.waset.org/abstracts/search?q=uniform%20step%20size" title=" uniform step size"> uniform step size</a>, <a href="https://publications.waset.org/abstracts/search?q=ordinary%20differential%20equations" title=" ordinary differential equations"> ordinary differential equations</a> </p> <a href="https://publications.waset.org/abstracts/16451/development-of-variable-order-block-multistep-method-for-solving-ordinary-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/16451.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">447</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3366</span> Reducing Uncertainty of Monte Carlo Estimated Fatigue Damage in Offshore Wind Turbines Using FORM</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jan-Tore%20H.%20Horn">Jan-Tore H. Horn</a>, <a href="https://publications.waset.org/abstracts/search?q=J%C3%B8rgen%20Juncher%20Jensen"> Jørgen Juncher Jensen</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Uncertainties related to fatigue damage estimation of non-linear systems are highly dependent on the tail behaviour and extreme values of the stress range distribution. By using a combination of the First Order Reliability Method (FORM) and Monte Carlo simulations (MCS), the accuracy of the fatigue estimations may be improved for the same computational efforts. The method is applied to a bottom-fixed, monopile-supported large offshore wind turbine, which is a non-linear and dynamically sensitive system. Different curve fitting techniques to the fatigue damage distribution have been used depending on the sea-state dependent response characteristics, and the effect of a bi-linear S-N curve is discussed. Finally, analyses are performed on several environmental conditions to investigate the long-term applicability of this multistep method. Wave loads are calculated using state-of-the-art theory, while wind loads are applied with a simplified model based on rotor thrust coefficients. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fatigue%20damage" title="fatigue damage">fatigue damage</a>, <a href="https://publications.waset.org/abstracts/search?q=FORM" title=" FORM"> FORM</a>, <a href="https://publications.waset.org/abstracts/search?q=monopile" title=" monopile"> monopile</a>, <a href="https://publications.waset.org/abstracts/search?q=Monte%20Carlo" title=" Monte Carlo"> Monte Carlo</a>, <a href="https://publications.waset.org/abstracts/search?q=simulation" title=" simulation"> simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=wind%20turbine" title=" wind turbine"> wind turbine</a> </p> <a href="https://publications.waset.org/abstracts/47967/reducing-uncertainty-of-monte-carlo-estimated-fatigue-damage-in-offshore-wind-turbines-using-form" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/47967.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">260</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3365</span> On the Approximate Solution of Continuous Coefficients for Solving Third Order Ordinary Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20M.%20Sagir">A. M. Sagir</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y^'''= f(x,y,y^',y^'' ), y(α)=y_0,〖y〗^' (α)=β,y^('' ) (α)=μ with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non-stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=block%20method" title="block method">block method</a>, <a href="https://publications.waset.org/abstracts/search?q=hybrid" title=" hybrid"> hybrid</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20multistep" title=" linear multistep"> linear multistep</a>, <a href="https://publications.waset.org/abstracts/search?q=self-starting" title=" self-starting"> self-starting</a>, <a href="https://publications.waset.org/abstracts/search?q=third%20order%20ordinary%20differential%20equations" title=" third order ordinary differential equations"> third order ordinary differential equations</a> </p> <a href="https://publications.waset.org/abstracts/3659/on-the-approximate-solution-of-continuous-coefficients-for-solving-third-order-ordinary-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/3659.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">271</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3364</span> Numerical Treatment of Block Method for the Solution of Ordinary Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20M.%20Sagir">A. M. Sagir</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=block%20method" title="block method">block method</a>, <a href="https://publications.waset.org/abstracts/search?q=first%20order%20ordinary%20differential%20equations" title=" first order ordinary differential equations"> first order ordinary differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=hybrid" title=" hybrid"> hybrid</a>, <a href="https://publications.waset.org/abstracts/search?q=self-starting" title=" self-starting "> self-starting </a> </p> <a href="https://publications.waset.org/abstracts/3426/numerical-treatment-of-block-method-for-the-solution-of-ordinary-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/3426.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">482</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3363</span> On the Construction of Some Optimal Binary Linear Codes</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Skezeer%20John%20B.%20Paz">Skezeer John B. Paz</a>, <a href="https://publications.waset.org/abstracts/search?q=Ederlina%20G.%20Nocon"> Ederlina G. Nocon</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Finding an optimal binary linear code is a central problem in coding theory. A binary linear code C = [n, k, d] is called optimal if there is no linear code with higher minimum distance d given the length n and the dimension k. There are bounds giving limits for the minimum distance d of a linear code of fixed length n and dimension k. The lower bound which can be taken by construction process tells that there is a known linear code having this minimum distance. The upper bound is given by theoretic results such as Griesmer bound. One way to find an optimal binary linear code is to make the lower bound of d equal to its higher bound. That is, to construct a binary linear code which achieves the highest possible value of its minimum distance d, given n and k. Some optimal binary linear codes were presented by Andries Brouwer in his published table on bounds of the minimum distance d of binary linear codes for 1 ≤ n ≤ 256 and k ≤ n. This was further improved by Markus Grassl by giving a detailed construction process for each code exhibiting the lower bound. In this paper, we construct new optimal binary linear codes by using some construction processes on existing binary linear codes. Particularly, we developed an algorithm applied to the codes already constructed to extend the list of optimal binary linear codes up to 257 ≤ n ≤ 300 for k ≤ 7. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=bounds%20of%20linear%20codes" title="bounds of linear codes">bounds of linear codes</a>, <a href="https://publications.waset.org/abstracts/search?q=Griesmer%20bound" title=" Griesmer bound"> Griesmer bound</a>, <a href="https://publications.waset.org/abstracts/search?q=construction%20of%20linear%20codes" title=" construction of linear codes"> construction of linear codes</a>, <a href="https://publications.waset.org/abstracts/search?q=optimal%20binary%20linear%20codes" title=" optimal binary linear codes"> optimal binary linear codes</a> </p> <a href="https://publications.waset.org/abstracts/31628/on-the-construction-of-some-optimal-binary-linear-codes" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/31628.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">755</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3362</span> Extension of Positive Linear Operator</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Manal%20Azzidani">Manal Azzidani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This research consideres the extension of special functions called Positive Linear Operators. the bounded linear operator which defined from normed space to Banach space will extend to the closure of the its domain, And extend identified linear functional on a vector subspace by Hana-Banach theorem which could be generalized to the positive linear operators. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=extension" title="extension">extension</a>, <a href="https://publications.waset.org/abstracts/search?q=positive%20operator" title=" positive operator"> positive operator</a>, <a href="https://publications.waset.org/abstracts/search?q=Riesz%20space" title=" Riesz space"> Riesz space</a>, <a href="https://publications.waset.org/abstracts/search?q=sublinear%20function" title=" sublinear function"> sublinear function</a> </p> <a href="https://publications.waset.org/abstracts/33220/extension-of-positive-linear-operator" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/33220.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">517</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3361</span> Reliability Prediction of Tires Using Linear Mixed-Effects Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Myung%20Hwan%20Na">Myung Hwan Na</a>, <a href="https://publications.waset.org/abstracts/search?q=Ho-%20Chun%20Song"> Ho- Chun Song</a>, <a href="https://publications.waset.org/abstracts/search?q=EunHee%20Hong"> EunHee Hong</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We widely use normal linear mixed-effects model to analysis data in repeated measurement. In case of detecting heteroscedasticity and the non-normality of the population distribution at the same time, normal linear mixed-effects model can give improper result of analysis. To achieve more robust estimation, we use heavy tailed linear mixed-effects model which gives more exact and reliable analysis conclusion than standard normal linear mixed-effects model. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=reliability" title="reliability">reliability</a>, <a href="https://publications.waset.org/abstracts/search?q=tires" title=" tires"> tires</a>, <a href="https://publications.waset.org/abstracts/search?q=field%20data" title=" field data"> field data</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20mixed-effects%20model" title=" linear mixed-effects model"> linear mixed-effects model</a> </p> <a href="https://publications.waset.org/abstracts/37815/reliability-prediction-of-tires-using-linear-mixed-effects-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/37815.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">563</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3360</span> Measuring Multi-Class Linear Classifier for Image Classification</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fatma%20Susilawati%20Mohamad">Fatma Susilawati Mohamad</a>, <a href="https://publications.waset.org/abstracts/search?q=Azizah%20Abdul%20Manaf"> Azizah Abdul Manaf</a>, <a href="https://publications.waset.org/abstracts/search?q=Fadhillah%20Ahmad"> Fadhillah Ahmad</a>, <a href="https://publications.waset.org/abstracts/search?q=Zarina%20Mohamad"> Zarina Mohamad</a>, <a href="https://publications.waset.org/abstracts/search?q=Wan%20Suryani%20Wan%20Awang"> Wan Suryani Wan Awang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A simple and robust multi-class linear classifier is proposed and implemented. For a pair of classes of the linear boundary, a collection of segments of hyper planes created as perpendicular bisectors of line segments linking centroids of the classes or part of classes. Nearest Neighbor and Linear Discriminant Analysis are compared in the experiments to see the performances of each classifier in discriminating ripeness of oil palm. This paper proposes a multi-class linear classifier using Linear Discriminant Analysis (LDA) for image identification. Result proves that LDA is well capable in separating multi-class features for ripeness identification. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=multi-class" title="multi-class">multi-class</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20classifier" title=" linear classifier"> linear classifier</a>, <a href="https://publications.waset.org/abstracts/search?q=nearest%20neighbor" title=" nearest neighbor"> nearest neighbor</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20discriminant%20analysis" title=" linear discriminant analysis"> linear discriminant analysis</a> </p> <a href="https://publications.waset.org/abstracts/51310/measuring-multi-class-linear-classifier-for-image-classification" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/51310.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">538</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3359</span> Sensitivity Analysis in Fuzzy Linear Programming Problems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=S.%20H.%20Nasseri">S. H. Nasseri</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Ebrahimnejad"> A. Ebrahimnejad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Fuzzy set theory has been applied to many fields, such as operations research, control theory, and management sciences. In this paper, we consider two classes of fuzzy linear programming (FLP) problems: Fuzzy number linear programming and linear programming with trapezoidal fuzzy variables problems. We state our recently established results and develop fuzzy primal simplex algorithms for solving these problems. Finally, we give illustrative examples. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20linear%20programming" title="fuzzy linear programming">fuzzy linear programming</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20numbers" title=" fuzzy numbers"> fuzzy numbers</a>, <a href="https://publications.waset.org/abstracts/search?q=duality" title=" duality"> duality</a>, <a href="https://publications.waset.org/abstracts/search?q=sensitivity%20analysis" title=" sensitivity analysis"> sensitivity analysis</a> </p> <a href="https://publications.waset.org/abstracts/16916/sensitivity-analysis-in-fuzzy-linear-programming-problems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/16916.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">565</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3358</span> A Spectral Decomposition Method for Ordinary Differential Equation Systems with Constant or Linear Right Hand Sides</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=R.%20B.%20Ogunrinde">R. B. Ogunrinde</a>, <a href="https://publications.waset.org/abstracts/search?q=C.%20C.%20Jibunoh"> C. C. Jibunoh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a spectral decomposition method is developed for the direct integration of stiff and nonstiff homogeneous linear (ODE) systems with linear, constant, or zero right hand sides (RHSs). The method does not require iteration but obtains solutions at any random points of t, by direct evaluation, in the interval of integration. All the numerical solutions obtained for the class of systems coincide with the exact theoretical solutions. In particular, solutions of homogeneous linear systems, i.e. with zero RHS, conform to the exact analytical solutions of the systems in terms of t. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=spectral%20decomposition" title="spectral decomposition">spectral decomposition</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20RHS" title=" linear RHS"> linear RHS</a>, <a href="https://publications.waset.org/abstracts/search?q=homogeneous%20linear%20systems" title=" homogeneous linear systems"> homogeneous linear systems</a>, <a href="https://publications.waset.org/abstracts/search?q=eigenvalues%20of%20the%20Jacobian" title=" eigenvalues of the Jacobian"> eigenvalues of the Jacobian</a> </p> <a href="https://publications.waset.org/abstracts/54215/a-spectral-decomposition-method-for-ordinary-differential-equation-systems-with-constant-or-linear-right-hand-sides" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/54215.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">330</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3357</span> Fuzzy Linear Programming Approach for Determining the Production Amounts in Food Industry</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=B.%20G%C3%BCney">B. Güney</a>, <a href="https://publications.waset.org/abstracts/search?q=%C3%87.%20Teke"> Ç. Teke</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In recent years, rapid and correct decision making is crucial for both people and enterprises. However, uncertainty makes decision-making difficult. Fuzzy logic is used for coping with this situation. Thus, fuzzy linear programming models are developed in order to handle uncertainty in objective function and the constraints. In this study, a problem of a factory in food industry is investigated, required data is obtained and the problem is figured out as a fuzzy linear programming model. The model is solved using Zimmerman approach which is one of the approaches for fuzzy linear programming. As a result, the solution gives the amount of production for each product type in order to gain maximum profit. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=food%20industry" title="food industry">food industry</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20linear%20programming" title=" fuzzy linear programming"> fuzzy linear programming</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20logic" title=" fuzzy logic"> fuzzy logic</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20programming" title=" linear programming "> linear programming </a> </p> <a href="https://publications.waset.org/abstracts/27880/fuzzy-linear-programming-approach-for-determining-the-production-amounts-in-food-industry" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/27880.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">650</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3356</span> Variogram Fitting Based on the Wilcoxon Norm</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hazem%20Al-Mofleh">Hazem Al-Mofleh</a>, <a href="https://publications.waset.org/abstracts/search?q=John%20Daniels"> John Daniels</a>, <a href="https://publications.waset.org/abstracts/search?q=Joseph%20McKean"> Joseph McKean</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Within geostatistics research, effective estimation of the variogram points has been examined, particularly in developing robust alternatives. The parametric fit of these variogram points which eventually defines the kriging weights, however, has not received the same attention from a robust perspective. This paper proposes the use of the non-linear Wilcoxon norm over weighted non-linear least squares as a robust variogram fitting alternative. First, we introduce the concept of variogram estimation and fitting. Then, as an alternative to non-linear weighted least squares, we discuss the non-linear Wilcoxon estimator. Next, the robustness properties of the non-linear Wilcoxon are demonstrated using a contaminated spatial data set. Finally, under simulated conditions, increasing levels of contaminated spatial processes have their variograms points estimated and fit. In the fitting of these variogram points, both non-linear Weighted Least Squares and non-linear Wilcoxon fits are examined for efficiency. At all levels of contamination (including 0%), using a robust estimation and robust fitting procedure, the non-weighted Wilcoxon outperforms weighted Least Squares. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=non-linear%20wilcoxon" title="non-linear wilcoxon">non-linear wilcoxon</a>, <a href="https://publications.waset.org/abstracts/search?q=robust%20estimation" title=" robust estimation"> robust estimation</a>, <a href="https://publications.waset.org/abstracts/search?q=variogram%20estimation" title=" variogram estimation"> variogram estimation</a>, <a href="https://publications.waset.org/abstracts/search?q=wilcoxon%20norm" title=" wilcoxon norm"> wilcoxon norm</a> </p> <a href="https://publications.waset.org/abstracts/50377/variogram-fitting-based-on-the-wilcoxon-norm" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/50377.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">458</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3355</span> A General Approach to Define Adjoint of Linear and Non-linear Operators</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mehdi%20Jafari%20Matehkolaee">Mehdi Jafari Matehkolaee</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we have obtained the adjoint of an arbitrary operator (linear and nonlinear) in Hilbert space by introducing an n-dimensional Riemannian manifold. This general formalism covers every linear operator (non – differential) in Hilbert space. In fact, our approach shows that instead of using the adjoint definition of an operator directly, it can be obtained directly by relying on a suitable generalized space according to the action of the operator in question. For the case of nonlinear operators, we have to change the definition of the linear operator adjoint. But here, we have obtained an adjoint of these operators with respect to the definition of the derivative of the operator. As a matter of fact, we have shown one of the straight applications of the ''Frechet derivative'' in the algebra of the operators. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=adjoint%20operator" title="adjoint operator">adjoint operator</a>, <a href="https://publications.waset.org/abstracts/search?q=non-linear%20operator" title=" non-linear operator"> non-linear operator</a>, <a href="https://publications.waset.org/abstracts/search?q=differentiable%20operator" title=" differentiable operator"> differentiable operator</a>, <a href="https://publications.waset.org/abstracts/search?q=manifold" title=" manifold"> manifold</a> </p> <a href="https://publications.waset.org/abstracts/166456/a-general-approach-to-define-adjoint-of-linear-and-non-linear-operators" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/166456.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">119</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3354</span> Analytical Solution of Non–Autonomous Discrete Non-Linear Schrodinger Equation With Saturable Non-Linearity</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mishu%20Gupta">Mishu Gupta</a>, <a href="https://publications.waset.org/abstracts/search?q=Rama%20Gupta"> Rama Gupta</a> </p> <p class="card-text"><strong>Abstract:</strong></p> It has been elucidated here that non- autonomous discrete non-linear Schrödinger equation is associated with saturable non-linearity through photo-refractive media. We have investigated the localized solution of non-autonomous saturable discrete non-linear Schrödinger equations. The similarity transformation has been involved in converting non-autonomous saturable discrete non-linear Schrödinger equation to constant-coefficient saturable discrete non-linear Schrödinger equation (SDNLSE), whose exact solution is already known. By back substitution, the solution of the non-autonomous version has been obtained. We have analysed our solution for the hyperbolic and periodic form of gain/loss term, and interesting results have been obtained. The most important characteristic role is that it helps us to analyse the propagation of electromagnetic waves in glass fibres and other optical wave mediums. Also, the usage of SDNLSE has been seen in tight binding for Bose-Einstein condensates in optical mediums. Even the solutions are interrelated, and its properties are prominently used in various physical aspects like optical waveguides, Bose-Einstein (B-E) condensates in optical mediums, Non-linear optics in photonic crystals, and non-linear kerr–type non-linearity effect and photo refracting medium. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=B-E-Bose-Einstein" title="B-E-Bose-Einstein">B-E-Bose-Einstein</a>, <a href="https://publications.waset.org/abstracts/search?q=DNLSE-Discrete%20non%20linear%20schrodinger%20equation" title=" DNLSE-Discrete non linear schrodinger equation"> DNLSE-Discrete non linear schrodinger equation</a>, <a href="https://publications.waset.org/abstracts/search?q=NLSE-non%20linear%20schrodinger%20equation" title=" NLSE-non linear schrodinger equation"> NLSE-non linear schrodinger equation</a>, <a href="https://publications.waset.org/abstracts/search?q=SDNLSE%20-%20saturable%20discrete%20non%20linear%20Schrodinger%20equation" title=" SDNLSE - saturable discrete non linear Schrodinger equation"> SDNLSE - saturable discrete non linear Schrodinger equation</a> </p> <a href="https://publications.waset.org/abstracts/121074/analytical-solution-of-non-autonomous-discrete-non-linear-schrodinger-equation-with-saturable-non-linearity" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/121074.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">155</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3353</span> System of Linear Equations, Gaussian Elimination</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Rabia%20Khan">Rabia Khan</a>, <a href="https://publications.waset.org/abstracts/search?q=Nargis%20Munir"> Nargis Munir</a>, <a href="https://publications.waset.org/abstracts/search?q=Suriya%20Gharib"> Suriya Gharib</a>, <a href="https://publications.waset.org/abstracts/search?q=Syeda%20Roshana%20Ali"> Syeda Roshana Ali</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper linear equations are discussed in detail along with elimination method. Gaussian elimination and Gauss Jordan schemes are carried out to solve the linear system of equation. This paper comprises of matrix introduction, and the direct methods for linear equations. The goal of this research was to analyze different elimination techniques of linear equations and measure the performance of Gaussian elimination and Gauss Jordan method, in order to find their relative importance and advantage in the field of symbolic and numeric computation. The purpose of this research is to revise an introductory concept of linear equations, matrix theory and forms of Gaussian elimination through which the performance of Gauss Jordan and Gaussian elimination can be measured. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=direct" title="direct">direct</a>, <a href="https://publications.waset.org/abstracts/search?q=indirect" title=" indirect"> indirect</a>, <a href="https://publications.waset.org/abstracts/search?q=backward%20stage" title=" backward stage"> backward stage</a>, <a href="https://publications.waset.org/abstracts/search?q=forward%20stage" title=" forward stage"> forward stage</a> </p> <a href="https://publications.waset.org/abstracts/33569/system-of-linear-equations-gaussian-elimination" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/33569.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">595</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3352</span> Use of Linear Programming for Optimal Production in a Production Line in Saudi Food Co.</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Qasim%20M.%20Kriri">Qasim M. Kriri</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Few Saudi Arabia production companies face financial profit issues until this moment. This work presents a linear integer programming model that solves a production problem of a Saudi Food Company in Saudi Arabia. An optimal solution to the above-mentioned problem is a Linear Programming solution. In this regard, the main purpose of this project is to maximize profit. Linear Programming Technique has been used to derive the maximum profit from production of natural juice at Saudi Food Co. The operations of production of the company were formulated and optimal results are found out by using Lindo Software that employed Sensitivity Analysis and Parametric linear programming in order develop Linear Programming. In addition, the parameter values are increased, then the values of the objective function will be increased. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=parameter%20linear%20programming" title="parameter linear programming">parameter linear programming</a>, <a href="https://publications.waset.org/abstracts/search?q=objective%20function" title=" objective function"> objective function</a>, <a href="https://publications.waset.org/abstracts/search?q=sensitivity%20analysis" title=" sensitivity analysis"> sensitivity analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=optimize%20profit" title=" optimize profit"> optimize profit</a> </p> <a href="https://publications.waset.org/abstracts/86104/use-of-linear-programming-for-optimal-production-in-a-production-line-in-saudi-food-co" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/86104.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">205</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3351</span> New Segmentation of Piecewise Linear Regression Models Using Reversible Jump MCMC Algorithm</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Suparman">Suparman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Piecewise linear regression models are very flexible models for modeling the data. If the piecewise linear regression models are matched against the data, then the parameters are generally not known. This paper studies the problem of parameter estimation of piecewise linear regression models. The method used to estimate the parameters of picewise linear regression models is Bayesian method. But the Bayes estimator can not be found analytically. To overcome these problems, the reversible jump MCMC algorithm is proposed. Reversible jump MCMC algorithm generates the Markov chain converges to the limit distribution of the posterior distribution of the parameters of picewise linear regression models. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of picewise linear regression models. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=regression" title="regression">regression</a>, <a href="https://publications.waset.org/abstracts/search?q=piecewise" title=" piecewise"> piecewise</a>, <a href="https://publications.waset.org/abstracts/search?q=Bayesian" title=" Bayesian"> Bayesian</a>, <a href="https://publications.waset.org/abstracts/search?q=reversible%20Jump%20MCMC" title=" reversible Jump MCMC"> reversible Jump MCMC</a> </p> <a href="https://publications.waset.org/abstracts/31651/new-segmentation-of-piecewise-linear-regression-models-using-reversible-jump-mcmc-algorithm" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/31651.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">521</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3350</span> Least Squares Solution for Linear Quadratic Gaussian Problem with Stochastic Approximation Approach</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sie%20Long%20Kek">Sie Long Kek</a>, <a href="https://publications.waset.org/abstracts/search?q=Wah%20June%20Leong"> Wah June Leong</a>, <a href="https://publications.waset.org/abstracts/search?q=Kok%20Lay%20Teo"> Kok Lay Teo</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Linear quadratic Gaussian model is a standard mathematical model for the stochastic optimal control problem. The combination of the linear quadratic estimation and the linear quadratic regulator allows the state estimation and the optimal control policy to be designed separately. This is known as the separation principle. In this paper, an efficient computational method is proposed to solve the linear quadratic Gaussian problem. In our approach, the Hamiltonian function is defined, and the necessary conditions are derived. In addition to this, the output error is defined and the least-square optimization problem is introduced. By determining the first-order necessary condition, the gradient of the sum squares of output error is established. On this point of view, the stochastic approximation approach is employed such that the optimal control policy is updated. Within a given tolerance, the iteration procedure would be stopped and the optimal solution of the linear-quadratic Gaussian problem is obtained. For illustration, an example of the linear-quadratic Gaussian problem is studied. The result shows the efficiency of the approach proposed. In conclusion, the applicability of the approach proposed for solving the linear quadratic Gaussian problem is highly demonstrated. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=iteration%20procedure" title="iteration procedure">iteration procedure</a>, <a href="https://publications.waset.org/abstracts/search?q=least%20squares%20solution" title=" least squares solution"> least squares solution</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20quadratic%20Gaussian" title=" linear quadratic Gaussian"> linear quadratic Gaussian</a>, <a href="https://publications.waset.org/abstracts/search?q=output%20error" title=" output error"> output error</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20approximation" title=" stochastic approximation"> stochastic approximation</a> </p> <a href="https://publications.waset.org/abstracts/113018/least-squares-solution-for-linear-quadratic-gaussian-problem-with-stochastic-approximation-approach" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/113018.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">186</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3349</span> Airy Wave Packet for a Particle in a Time-Dependant Linear Potential </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Berrehail">M. Berrehail</a>, <a href="https://publications.waset.org/abstracts/search?q=F.%20Benamira"> F. Benamira</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We study the quantum motion of a particle in the presence of a time- dependent linear potential using an operator invariant that is quadratic in p and linear in q within the framework of the Lewis-Riesenfeld invariant, The special invariant operator proposed in this work is demonstrated to be an Hermitian operator which has an Airy wave packet as its Eigenfunction <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=airy%20wave%20packet" title="airy wave packet">airy wave packet</a>, <a href="https://publications.waset.org/abstracts/search?q=ivariant" title=" ivariant"> ivariant</a>, <a href="https://publications.waset.org/abstracts/search?q=time-dependent%20linear%20potential" title=" time-dependent linear potential"> time-dependent linear potential</a>, <a href="https://publications.waset.org/abstracts/search?q=unitary%20transformation" title=" unitary transformation"> unitary transformation</a> </p> <a href="https://publications.waset.org/abstracts/31077/airy-wave-packet-for-a-particle-in-a-time-dependant-linear-potential" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/31077.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">492</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3348</span> A Fuzzy Programming Approach for Solving Intuitionistic Fuzzy Linear Fractional Programming Problem</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sujeet%20Kumar%20Singh">Sujeet Kumar Singh</a>, <a href="https://publications.waset.org/abstracts/search?q=Shiv%20Prasad%20Yadav"> Shiv Prasad Yadav</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper develops an approach for solving intuitionistic fuzzy linear fractional programming (IFLFP) problem where the cost of the objective function, the resources, and the technological coefficients are triangular intuitionistic fuzzy numbers. Here, the IFLFP problem is transformed into an equivalent crisp multi-objective linear fractional programming (MOLFP) problem. By using fuzzy mathematical programming approach the transformed MOLFP problem is reduced into a single objective linear programming (LP) problem. The proposed procedure is illustrated through a numerical example. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=triangular%20intuitionistic%20fuzzy%20number" title="triangular intuitionistic fuzzy number">triangular intuitionistic fuzzy number</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20programming%20problem" title=" linear programming problem"> linear programming problem</a>, <a href="https://publications.waset.org/abstracts/search?q=multi%20objective%20linear%20programming%20problem" title=" multi objective linear programming problem"> multi objective linear programming problem</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20mathematical%20programming" title=" fuzzy mathematical programming"> fuzzy mathematical programming</a>, <a href="https://publications.waset.org/abstracts/search?q=membership%20function" title=" membership function"> membership function</a> </p> <a href="https://publications.waset.org/abstracts/16411/a-fuzzy-programming-approach-for-solving-intuitionistic-fuzzy-linear-fractional-programming-problem" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/16411.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">566</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3347</span> Approximation of Analytic Functions of Several Variables by Linear K-Positive Operators in the Closed Domain</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tulin%20Coskun">Tulin Coskun</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We investigate the approximation of analytic functions of several variables in polydisc by the sequences of linear k-positive operators in Gadjiev sence. The approximation of analytic functions of complex variable by linear k-positive operators was tackled, and k-positive operators and formulated theorems of Korovkin's type for these operators in the space of analytic functions on the unit disc were introduced in the past. Recently, very general results on convergence of the sequences of linear k-positive operators on a simply connected bounded domain within the space of analytic functions were proved. In this presentation, we extend some of these results to the approximation of analytic functions of several complex variables by sequences of linear k-positive operators. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=analytic%20functions" title="analytic functions">analytic functions</a>, <a href="https://publications.waset.org/abstracts/search?q=approximation%20of%20analytic%20functions" title=" approximation of analytic functions"> approximation of analytic functions</a>, <a href="https://publications.waset.org/abstracts/search?q=Linear%20k-positive%20operators" title=" Linear k-positive operators"> Linear k-positive operators</a>, <a href="https://publications.waset.org/abstracts/search?q=Korovkin%20type%20theorems" title=" Korovkin type theorems"> Korovkin type theorems</a> </p> <a href="https://publications.waset.org/abstracts/53219/approximation-of-analytic-functions-of-several-variables-by-linear-k-positive-operators-in-the-closed-domain" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/53219.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">338</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3346</span> Online Robust Model Predictive Control for Linear Fractional Transformation Systems Using Linear Matrix Inequalities</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Peyman%20Sindareh%20Esfahani">Peyman Sindareh Esfahani</a>, <a href="https://publications.waset.org/abstracts/search?q=Jeffery%20Kurt%20Pieper"> Jeffery Kurt Pieper</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the problem of robust model predictive control (MPC) for discrete-time linear systems in linear fractional transformation form with structured uncertainty and norm-bounded disturbance is investigated. The problem of minimization of the cost function for MPC design is converted to minimization of the worst case of the cost function. Then, this problem is reduced to minimization of an upper bound of the cost function subject to a terminal inequality satisfying the <em>l</em><sub>2</sub>-norm of the closed loop system. The characteristic of the linear fractional transformation system is taken into account, and by using some mathematical tools, the robust predictive controller design problem is turned into a linear matrix inequality minimization problem. Afterwards, a formulation which includes an integrator to improve the performance of the proposed robust model predictive controller in steady state condition is studied. The validity of the approaches is illustrated through a robust control benchmark problem. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=linear%20fractional%20transformation" title="linear fractional transformation">linear fractional transformation</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20matrix%20inequality" title=" linear matrix inequality"> linear matrix inequality</a>, <a href="https://publications.waset.org/abstracts/search?q=robust%20model%20predictive%20control" title=" robust model predictive control"> robust model predictive control</a>, <a href="https://publications.waset.org/abstracts/search?q=state%20feedback%20control" title=" state feedback control"> state feedback control</a> </p> <a href="https://publications.waset.org/abstracts/69466/online-robust-model-predictive-control-for-linear-fractional-transformation-systems-using-linear-matrix-inequalities" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/69466.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">395</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3345</span> Penetration Depth Study of Linear Siloxanes through Human Skin</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=K.%20Szymkowska">K. Szymkowska</a>, <a href="https://publications.waset.org/abstracts/search?q=K.%20Mojsiewicz-%20Pie%C5%84kowska"> K. Mojsiewicz- Pieńkowska</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Siloxanes are a common ingredients in medicinal products used on the skin, as well as cosmetics. It is widely believed that the silicones are not capable of overcoming the skin barrier. The aim of the study was to verify the possibility of penetration and permeation of linear siloxanes through human skin and determine depth penetration limit of these compounds. Based on the results it was found that human skin is not a barrier for linear siloxanes. PDMS 50 cSt was not identified in the dermis suggests that this molecular size of silicones (3780Da) is safe when it is used in the skin formulations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=linear%20siloxanes" title="linear siloxanes">linear siloxanes</a>, <a href="https://publications.waset.org/abstracts/search?q=methyl%20siloxanes" title=" methyl siloxanes"> methyl siloxanes</a>, <a href="https://publications.waset.org/abstracts/search?q=skin%20penetration" title=" skin penetration"> skin penetration</a>, <a href="https://publications.waset.org/abstracts/search?q=skin%20permeation" title=" skin permeation"> skin permeation</a> </p> <a href="https://publications.waset.org/abstracts/47996/penetration-depth-study-of-linear-siloxanes-through-human-skin" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/47996.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span 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