A higher order numerical scheme for generalized fractional diffusion equations |
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Authors: | Qinxu Ding Patricia J. Y. Wong |
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Affiliation: | School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore |
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Abstract: | In this article, we develop a higher order approximation for the generalized fractional derivative that includes a scale function z(t) and a weight function w(t). This is then used to solve a generalized fractional diffusion problem numerically. The stability and convergence analysis of the numerical scheme are conducted by the energy method. It is proven that the temporal convergence order is 3 and this is the best result to date. Finally, we present four examples to confirm the theoretical results. |
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Keywords: | diffusion problem generalized fractional derivative generalized weighted and shifted Grünwald-Letnikov difference method numerical solution |
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