A collocation method based on the Bessel functions of the first kind for singular perturbated differential equations and residual correction |
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| Authors: | Şuayip Yüzbaşı |
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| Affiliation: | Department of Mathematics, Faculty of Science, Akdeniz University, TR‐07058 Antalya, Turkey |
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| 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. Copyright © 2014 JohnWiley & Sons, Ltd. |
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| Keywords: | singular perturbated differential equations boundary value problems the Bessel functions of the first kind Bessel collocation method collocation points residual correction subclass 65L11 34A30 34B05 65M70 34K28 |
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