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2 International Journal of Applied Mechanics and Engineering

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Numerical solution of singularly perturbed two parameter problems using exponential splines

Padmaja P., Aparna P., Gorla Rama Subba Reddy, Pothanna N.

International Journal of Applied Mechanics and Engineering

2021

Vol. 26, no. 2

160--172

In this paper, we have studied a method based on exponential splines for numerical solution of singularly perturbed two parameter boundary value problems. The boundary value problem is solved on a Shishkin mesh by using exponential splines. Numerical results are tabulated for different values of the perturbation parameters. From the numerical results, it is found that the method approximates the exact solution very well.

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.