Construction of Block Hybrid Backward Differentiation Formula for some Classes of Second Order Initial Value Problems

Abstract

This paper focuses on the derivation of a 2-step block hybrid backward differentiation formula for the general solution of second order ordinary differential equations. The new method was derived using the procedure of collocation and interpolation of power series at some selected grid and off-grid points. Basic properties of the method were examined and the method found to be zero stable, consistent and convergent. The method was tested on some classes of second order initial value problems and on comparing with the exact solutions, the method performed accurately with relatively small errors.