SIX-STEP SECOND DERIVATIVE NON-HYBRID BLOCK METHOD BACKWARD DIFFERENTIATION FORMULA FOR STIFF SYSTEMS

Abstract

This paper presents an advanced six-step linear multistep method of order five, based on second derivative non-hybrid block backward differentiation formula (BDF), developed for numerical solution of stiff systems of ordinary differential equations. The development of the multistep collocation approach is carried out using the matrix inversion techniques. The block structure facilitates simultaneous computation of multiple solution points, improving computational efficiency. Moreover, the power series is adopted as basis function for driving the discrete and continuous formulations. The analysis of the method such as consistency, zero-stability, order and error constants is presented, confirming its suitability for stiff systems. Numerical experiments on standard are tested on stiff and non-stiff ordinary differential equations showed the new method outperforms existing method in terms of accuracy.