A preconditioned implementation of pseudospectral methods on arbitrary grids
In this article a preconditioner for pseudospectral methods in terms of expansion coefficients on arbitrary grids is presented. The preconditioner is first developed for application in ordinary differential equations and then is generalized for partial differential equations. A fully discrete pseudospectral approximation is then used to solve bivariate problems. This preconditioner, in effect, makes the pseudospectral methods insensitive to specific grid points. The numerical results show the efficiency of the method.