A rational spectral method for the KdV equation on the half line

作者：Zhang Zhong Qiang; Ma He Ping^*

来源：Journal of Computational and Applied Mathematics, 2009, 230(2): 614-625.

DOI：10.1016/j.cam.2009.01.025

• Spectral methods
• Petrov-Galerkin
• Rational functions
• KdV equation
• The half line

A Petrov-Galerkin method using orthogonal rational functions is proposed for the Korteweg-de Vries (KdV) equation on the half line with initial-boundary values. The nonlinear term and the right-hand side term are treated by Chebyshev rational interpolation explicitly, and the linear terms are computed with the Galerkin method implicitly. Such an approach is applicable using fast algorithms. Numerical results are presented for problems with both exponentially and algebraically decaying solutions, respectively, highlighting the performance of the proposed method.

• 出版日期2009-8-15
• 单位上海大学