A Six Step Block Method for Solution of Fourth Order Ordinary Differential Equations.

A linear multistep method for solving first order initial value problems of ordinary differential equations is presented in this paper. The approach of collocation approximation is adopted in the derivation of the scheme and then the scheme is applied as simultaneous integrator to first order initial value problems of ordinary differential equations. This implementation strategy is more accurate and efficient than those given when the same scheme is applied over overlapping intervals in predictor-corrector mode. Furthermore, the new block method possesses the desirable feature of the Runge-Kutta method of being self-starting and eliminates the use of the predictor-corrector method. Experimental results confirm the superiority of the new scheme over the existing methods.