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

A Compact Difference Scheme for an Evolution Equation with a Weakly Singular Kernel
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Year:    2012

Numerical Mathematics: Theory, Methods and Applications, Vol. 5 (2012), Iss. 4 : pp. 559–572

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.2012.m11032

Numerical Mathematics: Theory, Methods and Applications, Vol. 5 (2012), Iss. 4 : pp. 559–572

Published online:    2012-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    14

Keywords:    Evolution equation weakly singular kernel compact difference scheme stability convergence numerical experiment.

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