
Accession Number : ADA139310
Title : Exact Boundary Conditions at an Artificial Boundary for Partial Differential Equations in Cylinders.
Descriptive Note : Technical summary rept.,
Corporate Author : WISCONSIN UNIVMADISON MATHEMATICS RESEARCH CENTER
Personal Author(s) : Hagstrom,T ; Keller,H B
PDF Url : ADA139310
Report Date : Jan 1984
Pagination or Media Count : 32
Abstract : The numerical solution of partial differential equations in unbounded domains requires a finite computational domain. Often one obtains a finite domain by introducing an artificial boundary and imposing boundary conditions there. This paper derives exact boundary conditions at an artificial boundary for partial differential equations in cylinders. An abstract theory is developed to analyze the general linear problem. Solvability requirements and estimates of the solution of the resulting finite problem are obtained by use of the notions of exponential and ordinary dichotomies. Useful representations of the boundary conditions are derived using separation of variables for problems with constant tails. The constant tail results are extended to problems whose coefficients obtain limits at infinity by use of an abstract perturbation theory. The perturbation theory approach is also applied to a class of nonlinear problems. General asymptotic formulas for the boundary conditions are derived and displayed in detail. (Author)
Descriptors : *Boundary value problems, *Partial differential equations, Cylindrical bodies, Perturbation theory, Fluid flow, Applied mathematics, Domain walls
Subject Categories : Numerical Mathematics
Fluid Mechanics
Distribution Statement : APPROVED FOR PUBLIC RELEASE