A matrix-collocation method for solutions of singularly perturbed differential equations via Euler polynomials

Authors

DENİZ ELMACI
ŞUAYİP YÜZBAŞI
NURCAN BAYKUŞ SAVAŞANERİL

DOI

10.55730/1300-0098.3332

Abstract

In this paper, a matrix-collocation method which uses the Euler polynomials is introduced to find the approximate solutions of singularly perturbed two-point boundary-value problems (BVPs). A system of algebraic equations is obtained by converting the boundary value problem with the aid of the collocation points. After this algebraic system, the coefficients of the approximate solution are determined. This error analysis includes two theorems which consist of an upper bound of errors and an error estimation technique. The present method and error analysis are applied to three numerical examples of singularly perturbed two-point BVPs. Numerical examples and comparisons with other methods are given. These applications and comparisons show that the method gives effective results.

Keywords

Euler polynomials, singular perturbed differential equations, boundary value problems, error analysis, collocation method, matrix method

First Page

3260

Last Page

3275

Recommended Citation

ELMACI, DENİZ; YÜZBAŞI, ŞUAYİP; and SAVAŞANERİL, NURCAN BAYKUŞ (2022) "A matrix-collocation method for solutions of singularly perturbed differential equations via Euler polynomials," Turkish Journal of Mathematics: Vol. 46: No. 8, Article 14. https://doi.org/10.55730/1300-0098.3332
Available at: https://journals.tubitak.gov.tr/math/vol46/iss8/14