Electronic Journal of Differential Equations,
Conference 04 (2000), pp. 245-263.
Title: Localization of dependence for solutions of hyperbolic
differential equations
Author: Henry A. Warchall (Univ. of North Texas, Denton, TX, USA)
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.
Published July 12, 2000.
Math Subject Classifications: 35B30, 35L05, 35L15, 35L70, 35C10, 35A18, 35A35.
Key Words: Localization of dependence; wave equation;
computational domain boundary; exact nonreflecting boundary conditions.