ON CALCULATING SOLUTIONS OF QUASI-LINEAR, FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS

摘要

A common means to calculate solutions of non—linear hyperbolic partial differential equations, when shocks are present, is to introduce into an otherwise straightforward difference scheme special terms which might represent the action of a fictitious tempering mechanism, perhaps of some dissipative type. Experience seems to justify the use of such "tempered" schemes, but proofs of convergence are largely incomplete or lacking. In this paper, in the case of a simple type of equation, we shall give convergence proofs for a class of explicit tempering schemes including versions of the von Neumann-Richtmyer [7] and the Lax-Wendroff methods. These results supplement those of a previous paper devoted to tempering schemes of implicit type (and to an explicit scheme with linear viscosity).