Numerical solution of singular boundary value problems with logarithmic singularities by Padé approximation and collocation methods

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• 作者：Hassane Allouche ; ^{allouche_hassane@yahoo.fr" class="auth_mail" title="E-mail the corresponding author} ; Abderrahim Tazdayte ^{a.tazdayte@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Singularity ; Boundary value problems ; B-spline ; Padé ; approximation ; Superposed Padé ; approximation
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：311
• 期：Complete
• 页码：324-341
• 全文大小：553 K

文摘

In this paper, we present a method using quintic B-spline and Padé approximation for numerically solving singular boundary value problems, for certain ordinary differential equation having singular coefficient, we use the modified quintic B-spline to approximate the first coefficients in the Taylor expansion, on which all the other coefficients depend. Moreover, we introduce the superposed Padé approximation. The resulting perturbed initial value problem is then efficiently treated.