Legendre-Gauss-type spectral collocation algorithms for nonlinear ordinary/partial differential equations

摘要

We propose new Legendre-Gauss collocation algorithms for ordinary differential equations. We also design Legendre-Gauss-type collocation algorithms for time-dependent nonlinear partial differential equations. The suggested algorithms enjoy spectral accuracy in both time and space, and can be implemented in a fast and stable manner. Numerical results exhibit the effectiveness.