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Numerical Algorith. for Solving Multi-Pantograph.Delay Equations on th. h.lf-line Using Jacobi Rational Functions with.Convergence Analysis

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Acta Math.maticae Applicatae Sinica 2017年第2期33卷 297-310页

作者： Eid h. DOh. ali h. bhrawy Ramy M. h.FEZ Department of Math.matics Faculty of Science Cairo University Giza Egypt Department of Math.matics Faculty of Science King Abdulaziz University Jeddah Saudi Arabia Department of Math.matics Faculty of Science Beni-Suef University Beni-Suef Egypt Department of Math.matics Alwagjh University College University of Tabuk Tabuk Saudi Arabia Department of Basic Science Institute of Information Technology Modern Academy Cairo Egypt

A new spectral Jacobi rational-Gauss collocation （JRC） meth.d is proposed for solving th. multi- pantograph.delay differential equations on th. h.lf-line. Th. meth.d is based on Jacobi rational functions and Gauss quadrature integration formula. Th. main idea for obtaining a semi-analytical solution for th.se equations is essentially developed by reducing th. pantograph.equations with.th.ir initial conditions to systems of algebraic equations in th. unknown expansion coefficients. Th. convergence analysis of th. meth.d is analyzed. Th. meth.d possesses th. spectral accuracy. Numerical results indicating th. h.gh.accuracy and effectiveness of th.s algorith. are presented. Indeed, th. present meth.d is compared favorably with.oth.r meth.ds.

关键词： multi-pantograph.equation delay equation collocation meth.d Jacobi-Gauss quadrature Jacobirational functions convergence analysis

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A Jacobi Spectral Collocation Sch.me Based on Operational Matrix for Time-fractional Modified Korteweg-de Vries Equations

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Computer Modeling in Engineering & Sciences 2015年第3期104卷 185-209页

作者： A.h.bhrawy E.h.Doh. S.S.Ezz-Eldien M.A.Abdelkawy Department of Math.matics Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia Department of Math.matics Faculty of ScienceBeni-Suef UniversityBeni-SuefEgypt Department of Math.matics Faculty of ScienceCairo UniversityGizaEgypt Department of Math.matics Faculty of ScienceAssiut UniversityNew Valley BranchEl-Kharja 72511Egypt

In th.s paper,a h.gh.accurate numerical approach.is investigated for solving th. time-fractional linear and nonlinear Korteweg-de Vries(KdV)*** equations are th. most appropriate and desirable definition for ph.sical *** spectral collocation meth.d and th. operational matrix of fractional derivatives are used togeth.r with.th. h.lp of th. Gauss-quadrature formula in order to reduce such.problem into a problem consists of solving a system of algebraic equations wh.ch.greatly simplifying th. *** approach.is based on th. sh.fted Jacobi polynomials and th. fractional derivative is described in th. sense of *** addition,th. presented approach.is applied also to solve th. timefractional modified KdV *** testing th. accuracy,validity and applicability of th. developed numerical approach.we apply it to provide h.gh.accurate approximate solutions for four test problems.

关键词： KdV equation Jacobi polynomials Operational matrix Gauss quadrature Collocation spectral meth.d Caputo derivative

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