摘要
A generalized Gauss-type quadrature formula is introduced, which assists in selection of collocation points in pseudospectral method for differential equations with two-point derivative boundary conditions. Some results on the related Jacobi interpolation are established. A pseudospectral scheme is proposed for the Kuramoto-Sivashisky equation. A skew symmetric decomposition is used for dealing with the nonlinear convection term. The stability and convergence of the proposed scheme are proved. The error estimates are obtained. Numerical results show the efficiency of this approach.
A generalized Gauss-type quadrature formula is introduced, which assists in selection of collocation points in pseudospectral method for differential equations with two-point derivative boundary conditions. Some results on the related Jacobi interpolation are established. A pseudospectral scheme is proposed for the Kuramoto-Sivashisky equation. A skew symmetric decomposition is used for dealing with the nonlinear convection term. The stability and convergence of the proposed scheme are proved. The error estimates are obtained. Numerical results show the efficiency of this approach.
基金
TheworkofthefirstauthorispartiallysupportedbyShanghaiNaturalScienceFoundationN .0 0JC1 4 0 5 7,andShanghiNaturalScienceFoundationforYouthN .0 1QN85 .TheworkofthesecondauthorispartiallysupportedbytheSpecialFundsforMajorStateBasicResearchProjectsofChin
