Local Multisubscales and Delta Function (LMS-DF) Method to Improve Numerical Schemes for Hyperbolic Equations

Abstract

A new method to improve numerical schemes for solving hyperbolic equations is presented. In this method, multisubscales are locally opened in addition to the main-scale mesh, depending on the local magnitudes of the first and the second derivatives. Singular points such as sharp edge regions of curves are processed by using a delta functionlike treatment. Numerical results on the propagations of triangular and square waves are shown to clarify the usefulness of the method.