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Mathematics of Computation

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Numerical applications of reflection to partial differential equations

Author: Arthur David Snider
Journal: Math. Comp. 30 (1976), 220-240
MSC: Primary 65N99; Secondary 30A28, 65E05
MathSciNet review: 0443380
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Abstract: Recent papers have reported results on the numerical solution of nonlinear free boundary problems wherein a conformal transformation (which must be determined) maps the unknown flow region onto a known domain; the boundary conditions are handled by the method of steepest descent. The present paper discusses the use of the reflection property of solutions of elliptic equations to determine these boundary conditions. The procedure is applied to the vena contracta models, and it is seen that it converges about ten times faster than the steepest-descent method.

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Keywords: Reflection, free boundary, finite differences, conformal mapping
Article copyright: © Copyright 1976 American Mathematical Society