Computational Approach for a Singularly Perturbed Differential Equations With Mixed Shifts Using a Non-Polynomial Spline

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DOI: https://doi.org/10.28924/2291-8639-21-2023-5
Published: Jan 23, 2023
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Kumar Ragula, G. BSL Soujanya, D. Swarnakar, Computational Approach for a Singularly Perturbed Differential Equations With Mixed Shifts Using a Non-Polynomial Spline, Int. J. Anal. Appl., 21 (2023), 5.

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Kumar Ragula, G. BSL Soujanya, D. Swarnakar

Abstract

In this paper, a second order singularly perturbed differential difference equation with both the negative and positive shifts is considered. A fitted non-polynomial spline approach is applied to solve the problem. Taylor series expansion process is being used to produce an approximated form of the considered problem, and then a fitted non-polynomial spline approach is devised in the form of a three-term recurrence relation. The convergence of the method is examined, and a quadratic rate of convergence is achieved. The maximum absolute error with quadratic rate of convergence of the solution is recorded. Layer profile is examined using the graphs.

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