Exponential spline method for singularly perturbed third-order boundary value problems-Reference-Cited by-同舟云学术

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

Published:2020-01-01 Issue:1 Volume:53 Page:360-372
ISSN:2391-4661
Container-title:Demonstratio Mathematica
language:en
Short-container-title:

Author:

Wakjira Yohannis Alemayehu¹,Duressa Gemechis File²

Affiliation:

1. Department of Mathematics, Dambi Dollo University , Dambi Dollo , P. O. Box 260 , Ethiopia

2. Department of Mathematics, Jimma University , Jimma , P. O. Box 378 , Ethiopia

Abstract

Abstract 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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/dema-2020-0024/pdf

Reference19 articles.

1. Ghazala Akram and Imran Talib, Quartic non-polynomial spline solution of a third order singularly perturbed boundary value problem, Res. J. App. Sci. Eng. Technol. 7 (2014), no. 23, 4859–4863, http://dx.doi.org/10.19026/rjaset.7.875.

2. Aynalem Tafere Chekole, Gemechis File Duresssa and Gashu Gadisa Kiltu, Non-polynomial septic spline method for singularly perturbed two point boundary value problems of order three, J. Taibah Univ. Sci. 13 (2019), no. 1, 651–660, https://doi.org/10.1080/16583655.2019.1617986.

3. Ghulam Mustafa and Syeda Tehmina Ejaz, A subdivision collocation method for solving two point boundary value problems of order three, J. Appl. Anal. Comput. 7 (2017), no. 3, 942–956, https://doi.org/10.11948/2017059.

4. Yohannis Alemayehu Wakjira, Gemechis File Duressa and Tesfaye Aga Bullo, Quintic non-polynomial spline method for third order singularly perturbed boundary value problems, J. King Saud Univ. Sci. 30 (2018), no. 1, 131–137, https://doi.org/10.1016/j.jksus.2017.01.008.

5. Arshad Khan and Pooja Khandelwal, Numerical solution of third order singularly perturbed boundary value problems using exponential quartic spline, Thai J. Math. 17 (2019), no. 3, 663–672.

Cited by 7 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Numerical solution of singularly perturbed singular third order boundary value problems with nonclassical sinc method;Results in Applied Mathematics;2024-05

2. A High-Resolution Exponential Spline Method and Its Convergence Analysis for Two-Point Mixed Boundary Value Problems;International Journal of Computational Methods;2024-04-30

3. Numerical Solution of Singularly Perturbed Singular Third Order Boundary Value Problems with Nonclassical Sinc Method;2024

4. Numerical solution of third order singular boundary value problems with nonclassical SE-sinc-collocation and nonclassical DE-sinc-collocation;Results in Applied Mathematics;2023-11

5. Numerical solution of third-Order boundary value problems using non-classical sinc-collocation method;COMPUT METHODS DIFFE;2023