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An intial-value technique for self-adjoint singularly perturbed two-point boundary value problems

Padmaja P., Aparna P., Gorla R. S. R.

International Journal of Applied Mechanics and Engineering

2020

Vol. 25, no. 1

106--126

In this paper, we present an initial value technique for solving self-adjoint singularly perturbed linearvboundary value problems. The original problem is reduced to its normal form and the reduced problem is converted to first order initial value problems. This replacement is significant from the computational point of view. The classical fourth order Runge-Kutta method is used to solve these initial value problems. This approach to solve singularly perturbed boundary-value problems is numerically very appealing. To demonstrate the applicability of this method, we have applied it on several linear examples with left-end boundary layer and rightend layer. From the numerical results, the method seems accurate and solutions to problems with extremely thin boundary layers are obtained.

Third order singularly perturbed delay differential equation of reaction diffusion type with integral boundary condition

Sekar Elango, Tamilselvan Ayyadurai

Journal of Applied Mathematics and Computational Mechanics

2019

Vol. 18, nr 2

99--110

A class of third order singularly perturbed delay differential equations of reaction diffusion type with an integral boundary condition is considered. A numerical method based on a finite difference scheme on a Shishkin mesh is presented. The method suggested is of almost first order convergent. An error estimate is derived in the discrete norm. Numerical examples are presented, which validate the theoretical estimates.