Time Discretization with Spatial Collocation Method for a Parabolic Integro-Differential Equation with a weakly Singular Kernel

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2006, v.13 no.1, pp.19-38

Kim Chang-Ho (DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE OF KONKUK UNIVERSITY)

Kim Chang-Ho. (2006). TIME DISCRETIZATION WITH SPATIAL COLLOCATION METHOD FOR A PARABOLIC INTEGRO-DIFFERENTIAL EQUATION WITH A WEAKLY SINGULAR KERNEL. 한국수학교육학회지시리즈B:순수및응용수학, 13(1), 19-38.

복사

Abstract

We analyze the spectral collocation approximation for a parabolic partial integrodifferential equations(PIDE) with a weakly singular kernel. The space discretization is based on the spectral collocation method and the time discretization is based on Crank-Nicolson scheme with a graded mesh. We obtain the stability and second order convergence result for fully discrete scheme.

keywords: integro-differential equation, weakly singular kernel, time discretization, spectral collocation method

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논문 상세

Vol.13 No.1

TIME DISCRETIZATION WITH SPATIAL COLLOCATION METHOD FOR A PARABOLIC INTEGRO-DIFFERENTIAL EQUATION WITH A WEAKLY SINGULAR KERNEL

Time Discretization with Spatial Collocation Method for a Parabolic Integro-Differential Equation with a weakly Singular Kernel

Abstract

한국수학교육학회지시리즈B:순수및응용수학