An accurate hybrid block technique for second order singular problems in ordinary differential equations

Abstract

A block hybrid method for solution of second order singular problems in ordinary differential equations is proposed in this work. For this purpose, two basis functions were combined for the development of a continuous hybrid schemes using collocation and interpolation technique. To make the continuous scheme self-starting, a block method of discrete hybrid form was derived. The scheme was analyzed using appropriate existing definitions to investigate their stability, consistency and convergence which were then shown to be consistent, zero-stable and hence convergent. Illustrative examples have been discussed to demonstrate the validity and applicability of the technique and the results have been compared with those of existing methods.