Two point fully implicit block method of variable step size is developed for solving directly the second order system of Ordinary Differential Equations (ODEs). This method will estimate the solutions of Initial Value Problems (IVPs) at two points simultaneously. The method developed is suitable for the numerical integration of non stiff and mildly stiff differential systems. Numerical results ...

Stabilized explicit methods are particularly efficient for large systems of stiff stochastic differential equations (SDEs) due to their extended stability domain. However, they loose efficiency when a severe stiffness is induced by very few fast degrees freedom, as the and nonstiff terms evaluated concurrently. Therefore, inspired [A. Abdulle, M. J. Grote, G. Rosilho de Souza, Preprint (2020), ...