Sequential and parallel methods for solving first-order hyperbolic equations

Abstract

Techniques for two-time level difference schemes are presented for the numerical solution of first-order hyperbolic partial differential equations. The space derivative is approximated by (i) a low-order, and (ii) a higher-order backward difference replacement, resulting in a system of first-order ordinary differential equations, the solutions of which satisfy recurrence relations. The methods are obtained from the recurrence relations and are tested on three linear problems and one non-linear problem from the literature.