Paper Info
Title
The reformulation and numerical solution of certain nonclassical initial-boundary value problems
Abstract
Several physical phenomena are modeled by nonclassical parabolic or hyperbolic initial-boundary value problems in one space variable which involve an integral over the spatial domain of a function of the desired solution or of its first spatial derivative. This integral may appear in the boundary conditions and/or the governing partial differential equation itself. In this paper, several examples of problems of this type, which arise in such diverse areas as chemical diffusion and heat conduction processes, thermoelasticity, population dynamics, vibration problems, nuclear reactor dynamics, and certain biological processes, are presented. In general, these problems are either not in the form required by widely available general-purpose software packages or the application of such software would be awkward and/or inefficient. It is shown how the example problems can be converted to a form to which existing software or standard numerical procedures may be applied in a relatively straightforward manner. Special attention is devoted to one particular problem, the diffusion equation subject to the specification of mass in a portion of the domain, which has been studied quite extensively, both analytically and numerically, in recent years. As an example of an effective method for the solution of the reformulated version of this problem, a finite-difference method based on Keller's box scheme is considered. Results of numerical experiments are presented which compare this scheme with a Crank-Nicolson finite-element Galerkin method proposed recently.
Year
DOI
Venue
1991
10.1137/0912007
SIAM Journal on Scientific Computing
Keywords
Field
DocType
NONCLASSICAL PARABOLIC AND HYPERBOLIC INITIAL-BOUNDARY VALUE PROBLEMS,NONLOCAL BOUNDARY CONDITIONS,PARTIAL INTEGRODIFFERENTIAL EQUATIONS,KELLER BOX SCHEME
Population,Boundary value problem,Mathematical optimization,Mathematical analysis,Galerkin method,Initial value problem,Finite difference method,Partial differential equation,Diffusion equation,Mathematics,Parabola
Journal
Volume
Issue
ISSN
12
1
0196-5204
Citations 
PageRank 
References 
11
4.12
4
Authors
2
Name
Order
Citations
PageRank
Graeme Fairweather116540.42
Rick D. Saylor2114.12