Abstract
We propose a highly accurate method to solve a class of singular two-point boundary-value problems having singular coefficients. These problems often arise when a partial differential equation is reduced to an ordinary differential equation by physical symmetry. The proposed method is based on Padé approximation and two-step collocation. The resolution domain is divided, Padé approximant is used on the subdomain in the vicinity of the singular point and provides a new boundary condition, and then, two-step quartic B-spline is used on the remaining subdomain where the problem is transformed to a regular boundary-value problem. The subdomains are chosen optimally using a suitable optimization procedure. Some examples are presented along with a comparison of the numerical results with other methods.
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Notes
This problem has been introduced according to the request of one of the anonymous reviewers.
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Allouche, H., Tazdayte, A. & Tigma, K. Highly Accurate Method for Solving Singular Boundary-Value Problems Via Padé Approximation and Two-Step Quartic B-Spline Collocation. Mediterr. J. Math. 16, 72 (2019). https://doi.org/10.1007/s00009-019-1342-x
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DOI: https://doi.org/10.1007/s00009-019-1342-x