An Accurate Scheme by Block Method for Third Order Ordinary Differential Equations.

A block linear multistep method for solving special third 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 special third order initial value problem 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 Runge-Kutta method of being self-starting and eliminates the use predictor-corrector method. Experimental results confirm the superiority of the new scheme over the existing methods. (Keywords: linear multistep methods, LMMs, odes, P-stability, Zero-stability, third order, IVPs, initial value