NUMERICAL RESULTS ON ALTERNATING DIRECTIONSHOOTING METHOD FOR NONLINEAR PARTIALDIFFERENTIAL EQUATIONS

Kim, Do-Hyun; Kim, Do-Hyun

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P-ISSN3059-0604
E-ISSN3059-1309
KCI

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ISSN : 3059-0604

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Vol.15 No.1

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NUMERICAL RESULTS ON ALTERNATING DIRECTION SHOOTING METHOD FOR NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

NUMERICAL RESULTS ON ALTERNATING DIRECTIONSHOOTING METHOD FOR NONLINEAR PARTIALDIFFERENTIAL EQUATIONS

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309

2008, v.15 no.1, pp.57-72

Kim, Do-Hyun (Department of Mathematics Education, Cheju National University)

Kim, Do-Hyun. (2008). NUMERICAL RESULTS ON ALTERNATING DIRECTION SHOOTING METHOD FOR NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS, 15(1), 57-72.

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Abstract

This paper is concerned with the numerical solutions to steady state nonlinear elliptical partial differential equations (PDE) of the form $u_{xx}+u_{yy}+Du_{x}+Eu_{y}+Fu=G$, where D, E, F are functions of x, y, u, $u_{x}$, and $u_{y}$, and G is a function of x and y. Dirichlet boundary conditions in a rectangular region are considered. We propose alternating direction shooting method for solving such nonlinear PDE. Numerical results show that the alternating direction shooting method performed better than the commonly used linearized iterative method.

keywords: ADS method, NPDE

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논문 상세

Vol.15 No.1

NUMERICAL RESULTS ON ALTERNATING DIRECTION SHOOTING METHOD FOR NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

NUMERICAL RESULTS ON ALTERNATING DIRECTIONSHOOTING METHOD FOR NONLINEAR PARTIALDIFFERENTIAL EQUATIONS

Abstract

한국수학교육학회지시리즈B:순수및응용수학