Boundary Value Technique for Finding Numerical Solution to Boundary Value Problems for Third Order Singularly Perturbed Ordinary Differential Equations

A class of singularly perturbed two point boundary value problems (BVPs) for third order ordinary differential equations is considered. The BVP is reduced to a weakly coupled system of one first order Ordinary Differential Equation (ODE) with a suitable initial condition and one second order singula...

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Bibliographic Details
Published inInternational journal of computer mathematics Vol. 79; no. 6; pp. 747 - 763
Main Authors Valarmathi, S., Ramanujam, N.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis Group 2002
Taylor and Francis
Subjects
Asymptotic Approximation
Boundary Layer
Classical Finite Difference Scheme
Exact sciences and technology
Exponentially Fitted Finite Difference Scheme
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Sciences and techniques of general use
Self Adjoint Boundary Value Problem
Singular Perturbation
Third Order Differential Equation
Third order equation
Boundary value problem
Asymptotic expansion
Differential equation
Two point boundary value problem
Singular perturbation
Maximum principle
Asymptotic approximation
Boundary layer
Finite difference method
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Summary:A class of singularly perturbed two point boundary value problems (BVPs) for third order ordinary differential equations is considered. The BVP is reduced to a weakly coupled system of one first order Ordinary Differential Equation (ODE) with a suitable initial condition and one second order singularly perturbed ODE subject to boundary conditions. In order to solve this system, a computational method is suggested in this paper. This method combines an exponentially fitted finite difference scheme and a classical finite difference scheme. The proposed method is distinguished by the fact that, first we divide the domain of definition of the differential equation into three subintervals called inner and outer regions. Then we solve the boundary value problem over these regions as two point boundary value problems. The terminal boundary conditions of the inner regions are obtained using zero order asymptotic expansion approximation of the solution of the problem. The present method can be extended to system of two equations, of which, one is a first order ODE and the other is a singularly perturbed second order ODE. Examples are presented to illustrate the method.
ISSN:0020-7160
1029-0265
DOI:10.1080/00207160211284