A best approximation for the solution of one‐dimensional variable‐coefficient Burgers' equation |
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Authors: | Fuxiang Li Minggen Cui |
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Affiliation: | 1. Department of Mathematics, Harbin Institute of Technology, Weihai, ShanDong, People's of Republic of China;2. Department of Mathematics, Harbin University of Science and Technology, Harbin, HeiLongJiang, People's Republic of China |
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Abstract: | In this article, an iterative method for the approximate solution to one‐dimensional variable‐coefficient Burgers' equation is proposed in the reproducing kernel space W(3,2). It is proved that the approximation wn(x,t) converges to the exact solution u(x,t) for any initial function w0(x,t) ε W(3,2), and the approximate solution is the best approximation under a complete normal orthogonal system . Moreover the derivatives of wn(x,t) are also uniformly convergent to the derivatives of u(x,t).© 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 |
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Keywords: | best approximation Burgers' equation reproducing kernel |
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