A Three Step Implicit Hybrid Linear Multistep Method for the Solution of Third Order Ordinary Differential Equations

A Linear Multistep Hybrid Method (LMHM) with continuous coefficients is considered and directly applied to solve third order Initial Value Problems (IVPs). The continuous method is used to obtain Multiple Finite Difference Methods (MFDMs) each of order 5 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 the existing methods is established numerically.