The main purpose of this work is to find for any non-negative measure,the relations betweent the Gauss-Radau and Gauss-Lobatto formula and Gauss formulae for the same measure.As applications,the author obtained the ex...The main purpose of this work is to find for any non-negative measure,the relations betweent the Gauss-Radau and Gauss-Lobatto formula and Gauss formulae for the same measure.As applications,the author obtained the explicit Gauss-Radau and Gauss-Lobatto formulae for the Jacolbi weight and the Gori-Micchelli weight.展开更多
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 resul...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.展开更多
文摘The main purpose of this work is to find for any non-negative measure,the relations betweent the Gauss-Radau and Gauss-Lobatto formula and Gauss formulae for the same measure.As applications,the author obtained the explicit Gauss-Radau and Gauss-Lobatto formulae for the Jacolbi weight and the Gori-Micchelli weight.
文摘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.
