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Spectral collocation methods for a partial integro-differential equation with a weakly singular kernel

Published online by Cambridge University Press:  17 February 2009

Chang Ho Kim  and
U Jin Choi
Chang Ho Kim
Affiliation:
Current address: Dept. of Applied Mathematics, Konkuk University, Chungju, Chungbuk 380–701, Korea.
U Jin Choi
Affiliation:
Department of Mathematics of KAIST, Kusong-Dong 373–1, Yousong-Gu, Taejon 305–701, Korea.
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Abstract

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We propose and analyze the spectral collocation approximation for the partial integro-differential equations with a weakly singular kernel. The space discretization is based on the pseudo-spectral method, which is a collocation method at the Gauss-Lobatto quadrature points. We prove unconditional stability and obtain the optimal error bounds which depend on the time step, the degree of polynomial and the Sobolev regularity of the solution.

Type
Research Article
Information
The ANZIAM Journal , Volume 39 , Issue 3 , January 1998 , pp. 408 - 430
Copyright
Copyright © Australian Mathematical Society 1998

References

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