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A Compact Difference Scheme for an Evolution Equation with a Weakly Singular Kernel

Published online by Cambridge University Press:  28 May 2015

Hongbin Chen  and
Da Xu
Hongbin Chen*
Affiliation:
Institute of Mathematics and Physics, College of Science, Central South University of Forestry and Technology, Changsha, 410004, Hunan, China
Da Xu*
Affiliation:
Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China), College of Mathematics and Computer Science, Hunan Normal University, Changsha, 410081, Hunan, China
*
Corresponding author.Email address:[email protected]
Corresponding author.Email address:[email protected]
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Abstract

This paper is concerned with a compact difference scheme with the truncation error of order 3/2 for time and order 4 for space to an evolution equation with a weakly singular kernel. The integral term is treated by means of the second order convolution quadrature suggested by Lubich. The stability and convergence are proved by the energy method. A numerical experiment is reported to verify the theoretical predictions.

Keywords

45K0565M0665M1265M15Evolution equationweakly singular kernelcompact difference schemestabilityconvergencenumerical experiment
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 5 , Issue 4 , November 2012 , pp. 559 - 572
Copyright
Copyright © Global Science Press Limited 2012

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