A family of non-uniform mesh tension spline methods for singularly perturbed two-point singular boundary value problems with significant first derivatives

In this paper, tension spline numerical methods are developed on a non-uniform mesh for the efficient numerical integration of singularly perturbed two-point singular boundary value problems. The proposed methods are applicable to problems both in rectangular and polar coordinates. Error analysis of a method is analyzed. Numerical experiments are presented to demonstrate the utility and the efficiency of the proposed computational procedure.