CINXE.COM

<!DOCTYPE html><html lang="en-US"><head><title>Just a moment...</title><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta http-equiv="X-UA-Compatible" content="IE=Edge"><meta name="robots" content="noindex,nofollow"><meta name="viewport" content="width=device-width,initial-scale=1"><style>*{box-sizing:border-box;margin:0;padding:0}html{line-height:1.15;-webkit-text-size-adjust:100%;color:#313131;font-family:system-ui,-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Helvetica Neue,Arial,Noto Sans,sans-serif,Apple Color Emoji,Segoe UI Emoji,Segoe UI Symbol,Noto Color Emoji}body{display:flex;flex-direction:column;height:100vh;min-height:100vh}.main-content{margin:8rem auto;max-width:60rem;padding-left:1.5rem}@media (width <= 720px){.main-content{margin-top:4rem}}.h2{font-size:1.5rem;font-weight:500;line-height:2.25rem}@media (width <= 720px){.h2{font-size:1.25rem;line-height:1.5rem}}#challenge-error-text{background-image:url(data:image/svg+xml;base64,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);background-repeat:no-repeat;background-size:contain;padding-left:34px}@media (prefers-color-scheme:dark){body{background-color:#222;color:#d9d9d9}}</style><meta http-equiv="refresh" content="120"></head><body class="no-js"><div class="main-wrapper" role="main"><div class="main-content"><noscript><div class="h2"><span id="challenge-error-text">Enable JavaScript and cookies to continue</span></div></noscript></div></div><script>(function(){window._cf_chl_opt={cvId: '3',cZone: "publications.waset.org",cType: 'non-interactive',cRay: '9134f3865f36d083',cH: 'CaWzbC0XgnadGWv6mliEh4IZJnJ.RpCBWiHOfLNjI2w-1739786645-1.2.1.1-6rtpe_ceUsm_lHlGuc9q5daIu13xhCsZP0fatYlw9qUQWiIFhR51k21RZsho9EXl',cUPMDTk: "\/search?q=numerical%20approaches&__cf_chl_tk=VR.uCQ67QAhV8xzMSMjgrR8Dc5E0SBgmpGQT3Kn3Qq4-1739786645-1.0.1.1-HSjoNRa8.bsqW9kb9B6Hmz7CdsG.rBo9.LMqmzWAJkQ",cFPWv: 'b',cITimeS: '1739786645',cTTimeMs: '1000',cMTimeMs: '120000',cTplC: 0,cTplV: 5,cTplB: 'cf',cK: "",fa: "\/search?q=numerical%20approaches&__cf_chl_f_tk=VR.uCQ67QAhV8xzMSMjgrR8Dc5E0SBgmpGQT3Kn3Qq4-1739786645-1.0.1.1-HSjoNRa8.bsqW9kb9B6Hmz7CdsG.rBo9.LMqmzWAJkQ",md: "Z4btqyPnaUbQdLH6bJW_ViqXX9ryZneZe9DbRuLgvi0-1739786645-1.2.1.1-w.oUH9RxRxb_tDbGAh4BCXm4SL5nzrhe9gEd_cCuBdDMBGOQmCxpvRi4ABMXIYZuXvmaS5nmYt_KbWgktc_AULiOsCDNKWBmah11P4ZF8RgRl0ObjoLR9Xfoh94TtXgTUgluzwp4OV6ZbUnLXeEoizmzjht1A9wnMB_OoYNoq1jyhx4BFn0DEWWU.zKMZIty_qy6ajjEpxLbUJ0YUTCxMvqii7LRHUsGX7q2FUtBm22jnmrkGrlLE8XmKx7mdC4yQhOdAex5ik_iJNqAjPM3pgK3YAydvHXSG.lSv43XfOP_rpTaXnp1FreWMxf9rfdg1e5nbm4B8eIWCBH3JXjSE.qr1hCt29VquZjUKiQ.U0azAU5hywze9g2HpljaMe3JxyDvbizWtzhQr.Dvo2ORd5uRe2J_z6S2tmXtfFLTTdxIQbNZ79Xhpy.vVTEH7fYm6WN_f6ISXGM4SJPw2oDuP.kLxGdCl2yWLlVajNPZUikZfywaGicp8Ttn5Zo7AKcS6vQp_phXnRY2s1wPsVTm1gmVailIYg.N7MwX0Bk2bs6RRZtWk6bi9VaR.WhyIrxwhKcf5XkA9r2O7XoMORxsTBVJr4C3OD9X.qA.txhH9N1rsZ1MDV2w_Qfjl2iTQ9C0_BGTVX1NAq7Mee.tvyXsP_zbgvLy7Vmnx_zkkqWkcswL_5_PuAPYxRrUHSnwmgvCAK0J8wiLpjHFSXkLmSsudQexTkCoDB3VIoYdbeyqyLPrnFUEKtmhLBiS84TbZdkxHXMtbykR6bXz7M8UeYi4YWKPk.mKqcwxCvWvtE9H_jo7nOlHNnGliHj.Slbv87Hb1IfXj70fC8E_u12mPDZLCAh6afnu.WDw3vtw7xfrhuyDWRMbuTUwBqFK_4Uy8u0R.kl791VprAIOiUA67S20zbIfKCNZ4tAIiEsvOdh62uEOr16KpIn034xRlaEhpGiOAeKBJWoyxN1XQBgsFDq2DyI5ZAkGAKfLZfhl.49.VED.VJDs2BFQ2E_48_fUK97O6fFoYv2Y588PTkn3tAP56zRz0vgul49sUe9vT0rozG46ql40.s9bKBfVYMR33MTEB_.xHe17rDeOFWvZcd_xjZng52IDImJwrMBc7LfPOFGAy8LB2UUBrByY_wMCJT371H_C_2rEFY_SrDBixcOQW19KjDrX3nS2jHD6z3dGl7kR_xhajRTfj4KNEV1ndi0RrjA4KihlnhZLs8ZZfynEJI.CJC8dXCj_OLPTyG.9asS2h3HbCTyASpopbHxyT1xM4u6QSD18afN_SPm9H0c6.f3OFT09.CLZB54dB.Z7QxVN73VYe1Kwx9rQTtHfGou3q8Rk.oqbcse1o9mTLjaC6hmR2tMcByEA4WB0MHK367LHONp1aAyyd4DSMylYI7dQzA04UsJ4sn2vbfDnbiqn7zcXQEuAWwIWgus9ji4U_3GyCWtNIXEowxe1i3oGwHMBKWb7RATmuNcpgZiw7AIqR1LI1rISGB84NFa2jwg7eciIaDSaeTXMH_id311c_ZKT8jOj4gVnQa5mgY8zr9.UzeN0znhygfem4BQSaFo.QNITlWTLvLnmCqsoLVE6o3uKdlAU1fKvMGusCaDEBk4Z..ZeX6oZEPNt3XZAYgK65thNwSqgzypm2qsTDFpM3ouCdOoGqh58k8xwnpdr4Yn3n036GXDHB5cTJWNkT8trWaNE2g8ROHoWtS6SycZWnwvyS63EXjZtm1y40LpSnnRWrMVC54R7gs5wIRsfObOXCK7I7g_0IX3xq2DiEKWC7ZORwDTxdP.yseg78Je4Ximw_QiWmYNDQ39.Kk1erPGJS8_fhDt7kcXp8vnciRTx4P.ngxAIVTXrpkReiHoRnsz9CsYJYDoyn6l6OcYejkdKCapg2A9m5eDIKacre73JxoqUNxJZs.65DHpl6kEIBLapeA",mdrd: "VHsIma6hvbworeWMGvXNkUkrC06_lkYMVC5MRvr1RpQ-1739786645-1.2.1.1-dH241lqtCu3F8XPIG06B1_j7aZYGBno2pRtREMfDDK0ffPo1Q3icS5Z_v7NwAe67FPGVIk8VDLcCxCzcc0wB4FksZxYAakm4Sn_xSQM0m2E8gtFsjfXmmgip8qyqqyfftfYSwGlTHm_7ku6tyo.eD4mLEPn15Gf43jDx7HA7mFMsmlkyBeYBuA.029w0BcLdq_xnRIR3pawhEuzs98G0GJ1r1AtX9wcnHukBn.ilAa.a.W3g171CGlZPg.vNHg8f_1Ga7wlsBW0Y6g3QURBadFEw1VWE0NvtwVuNX_pWZ8qXs2sNT1kPfLka87ZOX3jpIXQtI.UBiFnCAIBkug1W1cQTxjONvBH0DQitHonDtAo__RVa9hDXhCzm.F_pQDUDkpGQ0xU76oRuK3tyGZ3V1uS6IF.Z.jh99Iwnq3yJNFoLpOet89UPnrG.656YpRd_SfGYo2ASb2pzxkntCaDyRB7ultlZn.kn3Dpx9yJN5r2jfflReJP2l8Iq3pvsUckAH8iLkBU4rQE3sffjDoutNvn.tlLOV6kvhXzxKN9bvWl0vsgAEqlJfhpidPdDCaMPSrZRYox41aEuYzi.g.55mFQcIssSClppentQTmV_CO9xPM.jJZ.kdEgZKTiViBWhWYUpOf.9C79AKzWbH.Gy7oDxoAeGaPKnzjO.6yizmPyXoa7zj_APGpF._NdW8Q2H0TLEJuua62CyqPmFi0NNMOegQwx3aRr2SyrZoeWCj6j8B6Vu455Mb2RPUM8xm3QfvhWx3BBLxhO94eRKnPRDVtkKf7FsR8t1.LG1XrFLxEkiLufgG9sq2Q.4necIAqbly4w.a_QhIDAtDTLgipBUqOPwSF9dMiyUoa4ZL7HHwyK8bBCSTHobNtibXuNWT0IoySTyKAN0Y9Cc5gkzQAUiYVbGBW9ybPq0MOVQFYYbIlmkDxCqOGyjZ1JaShgLoSaGCyjl3vijV0TxVJzyMoUE3p.thmO4v0pVjnNuHq1tl7yc0pHi2tjV52AgPEelTj_Rk7Pny4DRUemuy4Aq.Hxb_LDa83oh6_LfUvugRoOqU.ASnQAXDT94AM9FtUZHaf.R.NEDLDsxraRqS1J7_6w36t48VxUZgcy9cGABC9KUc97YaqdApcjtY4bFlQa63Ix1vb50CjpYH9fCrm4at4rUTQlAL4zZMoIFoh_XneUd.EKnyN_trvaxV.agxx5vxWCTryldsm31bdoKq2BZFquGCF7XYXL_zifdn8HG58uGh73Z48NpOZmDED4Sf0ukxE_tlqGu7b1flci5gfPTRvNRttup_k21QLnFeqsbxQ15FX_dXPgzFJ.UppyTmF4IFDXV.0FPjvhQtpTYsqOTcHPf2c7oABExKOA2kWkQXXHeJZmif3H3vG1.4qCMwU9bhEUtPAzvRvPJMZxQ5PH.HJHwkbacJKWGwt8ZH0rpGbddqib2dIpXUnN0YOize4BMPB1JvkX2DQcbc3kA3RyBa0_iWYAUt57_7gOu2PAKsz5JjYlXjG0wNY2lTmc.kcCgFsW7s.7QcVL49nZNjcNTikseIlXRM6._f3m_qCMyddR4gF5ym4ObBXHO_kS8Atglc6bTjKb8HSb9V_7qU1iz9ul2OTV8gaRk5wkjbxn0K94YF32qqx0kM2uhFspVMLV73M0gv5625mFHMe6gCU6zfmUXRLpm_fRvSOajrrKWJy.8IxZDMTukhR2ucKY.Opy6_ExIa5bsZbfPSERWszu2qnipZTLfb6kf3rpgGXj_o.JzVCETgB0E82bu6Mv2A8NRlasKC5H9cJGkmNPofwB05qCxoS4070zovTi6CBTaZtyzGKFCkHzVoxwtChl8nu3sGLs7Vv.tlc2Xqs084P8jt0FEruS.C3QJRkRFK6CLjVIniJqqHC2qo38H5ZMgLVUR4J395LUJ5WDiM09_sL2ClgF6A5CKYdcYFopCXz1ulA5Tadmpm2iGbrDpEefq0lm27XPn"};var cpo = document.createElement('script');cpo.src = '/cdn-cgi/challenge-platform/h/b/orchestrate/chl_page/v1?ray=9134f3865f36d083';window._cf_chl_opt.cOgUHash = location.hash === '' && location.href.indexOf('#') !== -1 ? '#' : location.hash;window._cf_chl_opt.cOgUQuery = location.search === '' && location.href.slice(0, location.href.length - window._cf_chl_opt.cOgUHash.length).indexOf('?') !== -1 ? '?' : location.search;if (window.history && window.history.replaceState) {var ogU = location.pathname + window._cf_chl_opt.cOgUQuery + window._cf_chl_opt.cOgUHash;history.replaceState(null, null, "\/search?q=numerical%20approaches&__cf_chl_rt_tk=VR.uCQ67QAhV8xzMSMjgrR8Dc5E0SBgmpGQT3Kn3Qq4-1739786645-1.0.1.1-HSjoNRa8.bsqW9kb9B6Hmz7CdsG.rBo9.LMqmzWAJkQ" + window._cf_chl_opt.cOgUHash);cpo.onload = function() {history.replaceState(null, null, ogU);}}document.getElementsByTagName('head')[0].appendChild(cpo);}());</script></body></html>