Implicit Second Derivative Hybrid Backward Differentiation Formula for the Solution of Second Order Ordinary Differential Equations

A Hybrid Backward Differentiation Formula (HBDF) of uniform order ten is proposed for the solution of second order stiff Initial Value Problems (IVPs) is studied in this article. The approach adopted for the derivation of backward differentiation formulae involves interpolation and collocation at appropriate selected points. The proposed order ten HBDF for general second order ODEs was found to be consistent, zero-stable and convergent. Numerical evidences show that the method proposed here perform favorable when compared with existing scheme as it yielded better accuracy.