Fourth Derivative Block Method for Solving Two-point Singular Boundary Value Problems and Related Stiff Problems

This paper contains the formulation of an algorithm for solving two-point singular nonlinear boundary value problems of ordinary differential equations. This method is basically a fourth derivative block method obtained from the collocation and interpolation of an assumed derivatives and functional of a basis function. Its implementation was on the evaluation of derivatives of the given smooth first derivative function u'(t) up to the fourth derivative, at some points t. It is proved that the algorithm is consistent, zero-stable and convergent. Errors for uniform step lengths are also investigated and presented. Numerical examples are provided to show the efficiency of the algorithm.