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.