Singly diagonally implicit runge‐kutta method for time‐dependent reaction‐diffusion equation |
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Authors: | Wenyuan Liao Yulian Yan |
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Institution: | 1. Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada, T2N 1N4;2. Department of Physics, Zhangzhou Normal University, Zhangzhou, Fujian 363000, People's Republic of China |
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Abstract: | In this article, an efficient fourth‐order accurate numerical method based on Padé approximation in space and singly diagonally implicit Runge‐Kutta method in time is proposed to solve the time‐dependent one‐dimensional reaction‐diffusion equation. In this scheme, we first approximate the spatial derivative using the second‐order central finite difference then improve it to fourth‐order by applying Padé approximation. A three stage fourth‐order singly diagonally implicit Runge‐Kutta method is then used to solve the resulting system of ordinary differential equations. It is also shown that the scheme is unconditionally stable, and is suitable for stiff problems. Several numerical examples are solved by the scheme and the efficiency and accuracy of the new scheme are compared with two widely used high‐order compact finite difference methods. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1423–1441, 2011 |
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Keywords: | high‐order method finite difference method reaction‐diffusion equation Padé approximation singly diagonally implicit Runge‐Kutta method |
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