Mathematical Physics and Quantum Field Theory
Electron. J. Diff. Eqns., Conf. 04, 2000, pp. 245263.
Localization of dependence for solutions of hyperbolic differential equations
Henry A. Warchall
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
multipletime initialvalue problems for the wave equation in one space
dimension.
Published November 3, 2000.
Mathematics Subject Classifications: 35B30, 35L05, 35L15,
35L70, 35C10, 35A18, 35A35.
Key words: Localization of dependence, wave equation,
computational domain boundary, exact nonreflecting boundary conditions.
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Henry A. Warchall
Department of Mathematics
University of North Texas
Denton, TX 762031430
and
Division of Mathematical Sciences
National Science Foundation
4201 Wilson Boulevard
Arlington, VA 22230
email: hankw@unt.edu

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