Abstract
In this paper, we present a basis set approach by the Constrained Interpolation Profile (CIP) method to establish a systematic and simple method to get highly accurate numerical solutions of linear and nonlinear partial differential equations. This method uses a simple polynomial basis set, by which physical quantities are approximated with their values and derivatives associated with grid points. Nonlinear operations on functions are carried out in the framework of differential algebra. Then, introducing scalar products and requiring the residue to be orthogonal to the basis, the linear and nonlinear partial differential equations are reduced to ordinary differential equations for values and spatial derivatives. The method is tested on the linear and nonlinear Schrodinger equation and is proven to give highly accurate solutions.
