A compact ADI scheme for the two dimensional time fractional diffusion‐wave equation in polar coordinates |
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| Authors: | Seakweng Vong Zhibo Wang |
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| Affiliation: | 1. Department of Mathematics, University of Macau, Avenida da Universidade, Taipa, Macau, China;2. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, China |
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| Abstract: | In this article, we consider finite difference schemes for two dimensional time fractional diffusion‐wave equations on an annular domain. The problem is formulated in polar coordinates and, therefore, has variable coefficients. A compact alternating direction implicit scheme with  accuracy order is derived, where τ, h1, h2 are the temporal and spatial step sizes, respectively. The stability and convergence of the proposed scheme are studied using its matrix form by the energy method. Numerical experiments are presented to support the theoretical results. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1692–1712, 2015 |
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| Keywords: | alternating direction implicit method compact difference scheme energy method polar coordinates |
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