A new high order numerical approach for a class of nonlinear derivative dependent singular boundary value problems

Abstract

This paper is concerned with the design and analysis of a high order numerical method based on B-spline collocation approach to approximate the solution of a class of nonlinear derivative dependent singular two-point boundary value problems subjected to Neumann and Robin boundary conditions. Convergence result for the proposed method is established through Green's function approach. It is proved that the new method provides h6−order convergent approximation to the solution of the underlying problem. To validate this theoretical result, numerical experiments are carried out. It is shown that the rate of convergence of present method is two orders and four orders of magnitude higher when compared respectively to the uniform mesh B-spline collocation method and non-uniform mesh B-spline collocation method [41]. Moreover, the new method has shown its advantage (in terms of accuracy) over other existing methods [10,23,31,36,49] applied to the special cases of the problem.