A finite difference method for a non-local boundary value problem for two-dimensional heat equation

A second-order finite difference scheme is given for the numerical solution of a two-dimensional non-local boundary value problem for heat equation. Using a suitable transformation, the solution of this problem is equivalent to the solution of two other problems. The first problem which is a one-dim...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 112; no. 1; pp. 133 - 142
Main Author: Dehghan, Mehdi
Format: Journal Article
Language:English
Published: New York, NY Elsevier Inc 01.06.2000
Elsevier
Subjects:
Chemistry
Exact sciences and technology
Finite difference techniques
General and physical chemistry
Global analysis, analysis on manifolds
Heat conduction equation
Mathematical analysis
Mathematics
Modified equivalent analysis
Non-local boundary value problems
Nuemann's boundary conditions
Numerical analysis
Numerical analysis in abstract spaces
Numerical analysis. Scientific computation
Numerical integration procedures
Partial differential equations
Sciences and techniques of general use
The range of stability
Theory of reactions, general kinetics
Theory of reactions, general kinetics. Catalysis. Nomenclature, chemical documentation, computer chemistry
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
The range of stability
Partial differential equations
Non-local boundary value problems
Heat conduction equation
Numerical integration procedures
Finite difference techniques
Nuemann's boundary conditions
Modified equivalent analysis
Neumann problem
Numerical integration
Boundary value problem
Stability
Heat equation
Numerical solution
Diffusion equation
Two dimensional model
Partial differential equation
Finite difference method
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:A second-order finite difference scheme is given for the numerical solution of a two-dimensional non-local boundary value problem for heat equation. Using a suitable transformation, the solution of this problem is equivalent to the solution of two other problems. The first problem which is a one-dimensional non-local boundary value problem giving the value of μ through using a second-order finite difference scheme. Using this result, the second problem will be changed to a classical two-dimensional problem with Nuemann's boundary condition which will be solved numerically. The stability properties and truncation error of the new method are discussed and the results of numerical experiments are presented.
ISSN:0096-3003
1873-5649
DOI:10.1016/S0096-3003(99)00055-7