Mathematical Physics and Quantum Field Theory
Electron. J. Diff. Eqns., Conf. 04, 2000, pp. 245-263.
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
multiple-time initial-value 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 76203-1430 and Division of Mathematical Sciences National Science Foundation 4201 Wilson Boulevard Arlington, VA 22230 email: hankw@unt.edu |