A pseudospectral method for two-point boundary value problems

Pseudospectral collocation is employed for the numerical solution of nonlinear two-point boundary value problems with separated end conditions. Second-order finite difference schemes are used as preconditioners for the spectral calculation, and a solution of the discretized equations is obtained using versions of the defect correction principle. The method and a variant based on an adaptive grid technique are tested on a variety of sample problems and are shown to provide high accuracy with low storage requirements.