Mixed method via Padé approximation and optimal cubic B-spline collocation for solving non-linear singular boundary value problems

Abstract

In this paper, we formulate two numerical schemes for finding approximate solutions of non-linear singular two point boundary value problems arising in physiology. First, l’Hopital’s rule is applied to remove the singularity due to the type of boundary condition at the singular point, the modified problem is then efficiently treated using optimal one-step cubic B-spline collocation. In the second approach, Pade approximation is implemented in the vicinity of the singular point and a boundary condition at a point $$\delta $$ (near the singular point ) is derived. The new regular BVP is then efficiently treated in the remaining part of the interval using optimal one-step cubic B-spline.