| Helmhoz方程的Legendre展开方法 |
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| 引用本文： | 赵廷刚,马和平. Helmhoz方程的Legendre展开方法[J]. 上海大学学报(英文版), 2008, 12(1): 15-19. DOI: 10.1007/s 11741-008-0103-3 |
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| 作者姓名： | 赵廷刚 马和平 |
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| 作者单位： | [1]Department of Mathematics, Lanzhou City University, Lanzhou 730070, P. R. China [2]Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P. R. China |
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| 摘 要： | A spectral method based on the Legendre polynomials for solving Helmholz equations was proposed. With an explicit formula for the Legendre polynomials in terms of arbitrary order of their derivatives, the successive integration of the Legendre polynomials was represented by the Legendre polynomials. Then the method was formulized for secondorder differential equations in one dimension and two dimensions. Numerical results indicate that the suggested method is significantly accurate and in satisfactory agreement with the exact solution.
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| 关 键 词： | Helmholz方程 Legendre 展开方法 解题方法 |
| 文章编号： | 10.1007/s11741-008-0103-3 |
| 收稿时间： | 2006-06-20 |
| 修稿时间： | 2007-03-22 |
Legendre expansion method for Helmholz equations |
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| ZHAO Ting-gang,MA He-ping. Legendre expansion method for Helmholz equations[J]. Journal of Shanghai University(English Edition), 2008, 12(1): 15-19. DOI: 10.1007/s 11741-008-0103-3 |
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| Authors: | ZHAO Ting-gang MA He-ping |
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| Affiliation: | 1. Department of Mathematics, Lanzhou City University, Lanzhou 730070, P. R. China;Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P. R. China
2. Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P. R. China |
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| Abstract: | A spectral method based on the Legendre polynomials for solving Helmholz equations was proposed. Withan explicit formula for the Legendre polynomials in terms of arbitrary order of their derivatives, the successive integrationof the Legendre polynomials was represented by the Legendre polynomials. Then the method was formulized for second-order differential equations in one dimension and two dimensions. Numerical results indicate that the suggested method issignificantly accurate and in satisfactory agreement with the exact solution. |
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| Keywords: | Legendre polynomials spectral methods collocation Helmholz equation |
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