AN UNCONDITIONALLY STABLE FINITE DIFFERENCE SCHEME FOR EQUATIONS OF CONSERVATION LAW FORM

Abstract

This study presents a numerical scheme for solving one dimensional equations of conservation law form.  The Saulyev’s finite difference techniques are used to compute the solution.  Although the resulting difference equation do not appear explicit, a suitable use of the equation make it explicit.  It is shown that this explicit scheme is unconditionally stable.  A numerical example is presented to demonstrate the accuracy and efficiency of the proposed computational procedure.