A self-starting linear multistep method for a direct solution of the general second-order initial value problem

Abstract : A selfstarting hybrid linear multistep method for direct solution of the general second-order initial value problem is considered. The continuous method is used to obtain Multiple Finite Difference Methods (MFDMs) (each of order 7) which are combined as simultaneous numerical integrators to provide a direct solution to IVPs over sub-intervals which do not overlap. The convergence of the MFDMs is discussed by conveniently representing the MFDMs as a block method and verifying that the block method is zero-stable and consistent. The superiority of the MFDMs over published work is established numerically.