The numerical solution of non-linear singular boundary value problems arising in physiology

A class of non-linear singular ordinary differential equations, is solved by a new method based on non-polynomial cubic spline. We use the quesilinearization technique to reduce the given non-linear problem to a sequence of linear problems. We modify the resulting set of differential equations at the singular point then treat this set of boundary value problems by using non-polynomial cubic spline approximation. The resulting system of algebraic equations is solved by using a tri-diagonal solver. Computational results are provided to demonstrate the viability of the new method.