A fast numerical scheme for solving singular boundary value problems arising in various physical models

摘要

In this work, a fast numerical scheme is proposed for numerical solution of a general class of nonlinear singular boundary value problems (SBVPs), which describe various physical phenomena in applied science and engineering. It is worth noting that the standard cubic B-spline collocation method provides a second order convergent approximation to the solution of a second-order SBVP, while the proposed method provides a sixth-order convergent approximation. To demonstrate the applicability and accuracy of the method, we consider six nonlinear examples, including five real-life problems. It is shown that the experimental rate of convergence of present scheme is six and our method produces significantly more accurate results than the existing ones. Additionally, the CPU time for the method is provided.