The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)
- Volume 13 Issue 1 Serial No. 31
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- Pages.19-38
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- 2006
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- 1226-0657(pISSN)
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- 2287-6081(eISSN)
TIME DISCRETIZATION WITH SPATIAL COLLOCATION METHOD FOR A PARABOLIC INTEGRO-DIFFERENTIAL EQUATION WITH A WEAKLY SINGULAR KERNEL
- Kim Chang-Ho (DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE OF KONKUK UNIVERSITY)
- Published : 2006.02.01
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