An Implicit Boundary, Spectral Collocation Method for Eigenvalue Problem in Two Chebyshev Directions

摘要

This paper present sa multi-dimensional spectral collocation method for computing eigenvalue problems with homogeneous boundary conditiosn. The expansion of colloction algorithm in multi-dimensions is developed in the form of matrix multiplication. The boundary conditiosn are directly imposed on those differentiation matrices of two Chebyshev directiosn. This method is applied to the stability of a diffusion equation and a plane Poiseuille flow. Its stralight expansion from single dimension to multi-dimensions and simple implementation of boudnary conditions render this method a general and robust spectral collocation method. It can be applied to solve the time marching type linear problems. Thus, the boundary points and their related calculations at each time step can be omitted, while boundary conditions are still automatically satisfield.