A fourth order method for solving singularly perturbed boundary value problems using non-polynomial splines

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 15 فروردین 1401  

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2022.74627.1091

نویسندگان

Shahna Khan ¹؛ Arshad Khan²

¹Department of Mathematics, Sri Venkateswara College, University of Delhi, New Delhi, India.

²Department of Mathematics, Jamia Millia Islamia, New Delhi, India.

چکیده

In this paper, a class of second-order singularly perturbed interior layer problems is examined. Non-polynomial mixed spline is used to develop the tridiagonal scheme. The developed method is second as well as fourth-order accurate based on the parameters. Error analysis is also carried out. The method is shown to converge point-wise to the true solution with higher accuracy. Linear and nonlinear second-order singularly perturbed boundary value problems have been solved by the presented method. Five numerical illustrations are given to demonstrate the applicability of the proposed method. Absolute errors are given in tables which shows that our method is more efficient than previous existing methods.

کلیدواژه‌ها

Singularly perturbed؛ Second-order problems؛ Non-polynomial splines؛ Convergence