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A collocation method based on the Bessel functions of the first kind for singular perturbated differential equations and residual correction
Author(s) -
Yüzbaşı Şuayip
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3278
Subject(s) - mathematics , bessel function , collocation (remote sensing) , residual , collocation method , matrix (chemical analysis) , mathematical analysis , boundary value problem , orthogonal collocation , differential equation , ordinary differential equation , algorithm , computer science , materials science , machine learning , composite material
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.