Weighted finite difference methods for a class of space fractional partial differential equations with variable coefficients |
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Authors: | Zhiqing Ding Min Li |
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Institution: | a School of Mathematics and Computational Science, Xiangtan University, Hunan 411105, China b LSEC, ICMSEC, Academy of Mathematics and System Sciences, Academia Sinica, P.O. Box 2719, Beijing 100080, China |
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Abstract: | A class of weighted finite difference methods (WFDMs) for solving a class of initial-boundary value problems of space fractional partial differential equations with variable coefficients is presented. Their stability and convergence properties are considered. It is proven that the WFDMs are unconditionally-stable for , and conditionally-stable for , here r is the weighting parameter subjected to 0≤r≤1. Some convergence results are given. These methods, problems and results generalize the corresponding methods, problems and results given in 7], 8] and 10]. Some numerical examples are provided to show the effectiveness of the methods with different weighting parameters. |
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Keywords: | 65M06 65M12 65R20 26A33 |
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