Solution of nonlinear evolution problems by parallelized collocation-interpolation methods

This paper deals with the solution of initial-boundary value problems for nonlinear evolution equations. The solution technique is based on collocation-interpolation methods which are improved in order to reduce computational errors at fixed discretizations of the independent variables. The method consists in parallelizing the approximation of the space derivatives so that the same approximation is reached by a lower number of collocation points, and hence, by a lower computation time. The analysis includes a theoretical and computational estimate both of the approximation error and of the computational time.