The weighted continuous galerkin scheme for ordinary differential equations

Abstract

We introduce the Weighted Continuous Galerkin Scheme for initial value ordinary differential equations. This is an extension of the Continuous Galerkin Scheme, having an extra parameter for the purpose of error reduction. We prove convergence in the L 2 norm in the time variable in a new way, similar to (elliptic) finite element techniques. Using the optimal L 2 estimates, we then prove max norm convergence. Numerical evidence for the effectiveness of the proposed scheme is presented.