A computational method for solving boundary value problems for third-order singularly perturbed ordinary differential equations

Authors:
S. Valarmathi;N. Ramanujam
Affiliations:
Department of Mathematics, Bharathidasan University, Tiruchirappalli 620024, Tamil Nadu, India;Department of Mathematics, Bharathidasan University, Tiruchirappalli 620024, Tamil Nadu, India
Venue:
Applied Mathematics and Computation
Year:
2002

Citing 6
Cited 8

Approximate method for the numerical solution of singular perturbation problems

Applied Mathematics and Computation
Numerical solution of singular perturbation problems via deviation arguments

Applied Mathematics and Computation
Numerical treatment of singularity perturbed two point boundary value problems

Applied Mathematics and Computation
Singular perturbation methods for ordinary differential equations

Singular perturbation methods for ordinary differential equations
A computational method for solving singular perturbation problems

Applied Mathematics and Computation
A computational method for solving singularly perturbed turning point problems exhibiting twin boundary layers

Applied Mathematics and Computation

Asymptotic initial value methods for two-parameter singularly perturbed boundary value problems for second order ordinary differential equations

Applied Mathematics and Computation
An asymptotic numerical fitted mesh method for singularly perturbed third order ordinary differential equations of reaction-diffusion type

Applied Mathematics and Computation
An asymptotic numerical method for singularly perturbed third-order ordinary differential equations with a weak interior layer

International Journal of Computer Mathematics
A recent survey on computational techniques for solving singularly perturbed boundary value problems

International Journal of Computer Mathematics
Convergence analysis of a streamline diffusion method for a singularly perturbed convection-diffusion problem

WSEAS Transactions on Mathematics
An asymptotic hybrid difference scheme for singularly perturbed third and fourth order ordinary differential equations with discontinuous source term

Neural, Parallel & Scientific Computations
A boundary value technique for boundary value problems for singularly perturbed fourth-order ordinary differential equations

Computers & Mathematics with Applications
Uniform convergence of monotone difference scheme for a singularly perturbed third-order convection-diffusion equation

Neural, Parallel & Scientific Computations - Special issue on computational techniques for differential equations will applications

Quantified Score

Hi-index	0.48

Visualization

Abstract

Singularly perturbed two-point boundary value problems (SPBVPs) for third-order ordinary differential equations (ODEs) with a small parameter multiplying the highest derivative are considered. A numerical method is suggested in this paper to solve such problems. In this method, the given BVP is transformed into a system of two ODEs subject to suitable initial and boundary conditions. Then the domain of definition of the differential equation (a closed interval) is divided into two sub-intervals, which we call the inner region (boundary layer) and the outer region. Then the DE is solved in these intervals separately. The solutions obtained in these intervals are combined to give the solution in the whole interval. To obtain boundary conditions at the transition points (boundary values inside this interval) we use mostly the zeroth-order asymptotic expansion of the solution of the BVP or a suitable asymptotic expansion solution. First, the linear equations are considered and then the semi-linear equations. To solve semilinear equations Newton's method of quasi-linearisation is applied. Examples are provided to illustrate the method. The method is easy to implement and suitable for parallel computing.