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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Vydané v:	Journal of applied mathematics & computing Ročník 23; číslo 1-2; s. 141 - 152
Hlavní autori:	Valanarasu, T., Ramanujam, N.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Dordrecht Springer Nature B.V 01.01.2007
Predmet:	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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Abstract	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.
AbstractList	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.[PUBLICATION ABSTRACT] 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.
Author	Valanarasu, T. Ramanujam, N.
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Cites_doi	10.1007/BF00940053 10.1023/A:1022639003366 10.1201/9781482285727 10.1023/A:1021744025980 10.1023/A:1022118420907 10.1016/S0168-9274(99)00140-3 10.1007/978-3-662-03206-0 10.1007/BF00939534 10.1016/j.mcm.2005.01.025 10.1016/S0096-3003(02)00663-X 10.1016/j.cam.2003.09.033 10.1016/S0096-3003(02)00160-1 10.1142/2933 10.1080/03057920412331272171
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SubjectTerms	Approximation Asymptotic expansions Asymptotic properties Boundary value problems Construction Initial value problems Mathematical analysis Mathematical models Ordinary differential equations Studies
Title	An asymptotic initial value method for second order singular perturbation problems of convection-diffusion type with a discontinuous source term
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