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Legendre expansion method for Helmholz equations

Legendre expansion method for Helmholz equations
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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. 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.
作者 赵廷刚 马和平
机构地区 Department of Mathematics Department of Mathematics
出处 《Journal of Shanghai University(English Edition)》 CAS 2008年第1期15-19,共5页 上海大学学报（英文版）
基金 Project supported by the National Natural Science Foundation of China （Grant No.10471472）
关键词 Legendre polynomials spectral methods COLLOCATION Helmholz equation Legendre polynomials, spectral methods, collocation, Helmholz equation
分类号 O411.1 [理学—理论物理]
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Journal of Shanghai University(English Edition)
2008年 第1期

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