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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.13 No.1

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

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / 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
Kim, C. (2006). Time Discretization with Spatial Collocation Method for a Parabolic Integro-Differential Equation with a weakly Singular Kernel. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 13(1), 19-38.

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

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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