An asymptotic initial value method for second order singular perturbation problems of convection-diffusion type with a discontinuous source term

In this paper a numerical method is presented to solve singularly perturbed two points boundary value problems for second order ordinary differential equations consisting a discontinuous source term. First, in this method, an asymptotic expansion approximation of the solution of the boundary value p...

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Vydáno v:Journal of applied mathematics & computing Ročník 23; číslo 1-2; s. 141 - 152
Hlavní autoři: Valanarasu, T., Ramanujam, N.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Dordrecht Springer Nature B.V 01.01.2007
Témata:
Approximation
Asymptotic expansions
Asymptotic properties
Boundary value problems
Construction
Initial value problems
Mathematical analysis
Mathematical models
Ordinary differential equations
Studies
ISSN:1598-5865, 1865-2085
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Popis
Shrnutí:In this paper a numerical method is presented to solve singularly perturbed two points boundary value problems for second order ordinary differential equations consisting a discontinuous source term. First, in this method, an asymptotic expansion approximation of the solution of the boundary value problem is constructed using the basic ideas of a well known perturbation method WKB. Then some initial value problems and terminal value problems are constructed such that their solutions are the terms of this asymptotic expansion. These initial value problems are happened to be singularly perturbed problems and therefore fitted mesh method (Shishkin mesh) are used to solve these problems. Necessary error estimates are derived and examples provided to illustrate the method.
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ISSN:1598-5865
1865-2085
DOI:10.1007/BF02831964