Highly Accurate Method for Solving Singular Boundary-Value Problems Via Padé Approximation and Two-Step Quartic B-Spline Collocation

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 Pade approximation and two-step collocation. The resolution domain is divided, Pade 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.