Exponentially fitted tension spline method for singularly perturbed differential difference equations

Iranian Journal of Numerical Analysis and Optimization

مقاله 2، دوره 11، شماره 2 - شماره پیاپی 20، آذر 2021، صفحه 261-282   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2021.68227.1009

نویسندگان

M.M. Woldaregay^{* 1}؛ G.F. Duressa²

¹Department of Applied athematics, Adama Science and Technology University, Adama, Ethiopia.

²Department of Mathematics, Jimma University, Jimma, Ethiopia.

چکیده

In this article, singularly perturbed differential difference equations having delay and advance in the reaction terms are considered. The highest-order derivative term of the equation is multiplied by a perturbation parameter ε taking arbitrary values in the interval (0, 1]. For the small value of ε, the solution of the equation exhibits a boundary layer on the left or right side of the domain depending on the sign of the convective term. The terms with the shifts are approximated by using the Taylor series approximation.The resulting singularly perturbed boundary value problem is solved using an exponentially fitted tension spline method. The stability and uniform convergence of the scheme are discussed and proved. Numerical exam ples are considered for validating the theoretical analysis of the scheme. The developed scheme gives an accurate result with linear order uniform convergence.

کلیدواژه‌ها

Differential difference؛ Exponentially fitted؛ Singularly perturbed problem؛ Tension spline؛ Uniform convergence

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