## A collocation method based on the Bessel functions of the first kind for singular perturbated differential equations and residual correction

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.38, no.14, pp.3033-3042, 2015 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 38 Issue: 14
• Publication Date: 2015
• Doi Number: 10.1002/mma.3278
• Journal Name:
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Page Numbers: pp.3033-3042
• Keywords: singular perturbated differential equations, boundary value problems, the Bessel functions of the first kind, Bessel collocation method, collocation points, residual correction, BOUNDARY-VALUE-PROBLEMS, INTEGRODIFFERENTIAL EQUATIONS, ALGORITHM, SYSTEMS
• Akdeniz University Affiliated: Yes

#### Abstract

In this paper, a collocation method is given to solve singularly perturbated two-point boundary value problems. By
using the collocation points, matrix operations and the matrix relations of the Bessel functions of the first kind and their
derivatives, the boundary value problem is converted to a system of the matrix equations. By solving this system, the
approximate solution is obtained. Also, an error problem is constructed by the residual function, and it is solved by the
presented method. Thus, the error function is estimated, and the approximate solutions are improved. Finally, numerical
examples are given to show the applicability of the method, and also, our results are compared by existing results.

In this paper, a collocation method is given to solve singularly perturbated two-point boundary value problems. By using the collocation points, matrix operations and the matrix relations of the Bessel functions of the first kind and their derivatives, the boundary value problem is converted to a system of the matrix equations. By solving this system, the approximate solution is obtained. Also, an error problem is constructed by the residual function, and it is solved by the presented method. Thus, the error function is estimated, and the approximate solutions are improved. Finally, numerical examples are given to show the applicability of the method, and also, our results are compared by existing results. Copyright (C) 2014 John Wiley & Sons, Ltd.