The galerkin-collocation method for hyperbolic initial boundary value problems

Abstract

In this paper we implement a spectral method for solving initial boundary value problems which is in between the Galerkin and collocation methods. In this method the partial differential equation and initial and boundary conditions are collocated at an overdetermined set of points and the approximate solution is chosen to be the least-squares solution to this system of equations. The solution is obtained using preconditioned residual minimization. Numerical results for linear and nonlinear hyperbolic problems are provided. © 1994 Academic Press, Inc.