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Volume 5, Issue 4
A Compact Difference Scheme for an Evolution Equation with a Weakly Singular Kernel

Hongbin Chen & Da Xu

DOI: 10.4208/nmtma.2012.m11032

Numer. Math. Theor. Meth. Appl., 5 (2012), pp. 559-572.

Published online: 2012-05

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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

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

  • AMS Subject Headings

45K05, 65M06, 65M12, 65M15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-5-559, author = {Hongbin Chen and Da Xu}, title = {A Compact Difference Scheme for an Evolution Equation with a Weakly Singular Kernel}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2012}, volume = {5}, number = {4}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2012.m11032}, url = {http://global-sci.org/intro/article_detail/nmtma/5949.html} }
TY - JOUR T1 - A Compact Difference Scheme for an Evolution Equation with a Weakly Singular Kernel AU - Hongbin Chen & Da Xu JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 559 EP - 572 PY - 2012 DA - 2012/05 SN - 5 DO - http://doi.org/10.4208/nmtma.2012.m11032 UR - https://global-sci.org/intro/article_detail/nmtma/5949.html KW - Evolution equation, weakly singular kernel, compact difference scheme, stability, convergence, numerical experiment. AB -

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.

Hongbin Chen and Da Xu. (2012). A Compact Difference Scheme for an Evolution Equation with a Weakly Singular Kernel. Numerical Mathematics: Theory, Methods and Applications. 5 (4). 559-572. doi:10.4208/nmtma.2012.m11032
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