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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.

Exponential spline method for singularly perturbed third-order boundary value problems

Wakjira Yohannis Alemayehu, Duressa Gemechis File

Demonstratio Mathematica

2020

Vol. 53, nr 1

360--372

The exponential spline function is presented to find the numerical solution of third-order singularly perturbed boundary value problems. Convergence analysis of the method is briefly discussed, and it is shown to be sixth order convergence. To validate the applicability of the method, some model problems are solved for different values of the perturbation parameter, and the numerical results are presented both in tables and graphs. Furthermore, the present method gives more accurate solution than some methods existing in the literature.