Special Second Order Stiff Delay Differential Equations Directly Solved by Using Variable Stepsize Variable Order Technique

Less attention was made to solve special second order stiff delay differential equations (DDEs) directly. In this paper, the development of direct predictor-corrector variable stepsize variable order (DBVSVO) method is described to solve special second order stiff DDEs directly without reducing to first order equations. The predictor and corrector formulae is derived based on backward differentiation formulae (BDF) and represented in divided difference form. In order to achieve greater efficiency, the developed method is implemented using variable stepsize variable order (VSVO) technique. Numerical results are presented to show that the developed method is suitable for solving special second order stiff DDEs. For comparison purposes the same set of test examples are reduced to a system of the first order equations and solved using predictor-corrector variable stepsize variable order method based on backward differentiation formulae (BVSVO) method proposed by Mohd Isa et al. [1].