Formation of Multiple Off-Grid Points for the Treatment of Systems of Stiff Ordinary Differential Equations

This paper is concerned with the construction of two-step hybrid block Simpson's method with four off-grid points for the solutions of stiff systems of ordinary differential equations (ODEs). This is achieved by transforming a k-step multi-step method into continuous form and evaluating at various grid points to obtain the discrete schemes. The discrete schemes are applied as a block for simultaneous integration. The block matrix equation is A-stable and of order [7, 7, 7, 7, 7, 7]T. This order ‘p' is achieved by the aid of Maple13 software program. The performance of the method is demonstrated on some numerical experiments. The results revealed that the hybrid block Simpson's method is efficient, accurate and convergent on stiff problems.