A Total Variation Diminishing Hopmoc Scheme for Numerical Time Integration of Evolutionary Differential Equations

Abstract

This paper concentrates on a total variation diminishing Hopmoc scheme for numerical time integration of evolutionary differential equations. The Hopmoc method for numerical integration of parabolic partial differential equations with convective dominance is based on the concept of spatially decomposed meshes used in the Hopscotch method. In addition, the Hopmoc method uses the concept of integration along characteristic lines in a Semi-Lagrangian scheme based on the Modified Method of Characteristics. This work employs Total Variation Diminishing schemes in order to increase accuracy of the Hopmoc method. Thus, this paper shows that the Hopmoc method in conjunction with a Total Variation Diminishing scheme provides effective improvements over the original Hopmoc method.