Localization of dependence for solutions of hyperbolic differential equations

Abstract

We survey several results that localize the dependence of solutions to hyperbolic equations. These observations address questions that are central to numerical simulation of solutions on unbounded spatial domains. One result shows that in principle it is possible to numerically compute (the restriction of) a solution to a wave equation on an unbounded domain using only a bounded computational domain. Other results provide implementations of this fact in particular situations. In addition, we introduce a new diagrammatic way to generate explicit solutions to multiple-time initial-value problems for the wave equation in one space dimension.

Keywords

• Localization of dependence
• wave equation
• computational domain boundary
• exact nonreflecting boundary conditions.