A Linear Multistep Method with Continuous coefficients for Solving First Order Ordinary Differential Equation (ODE)

Abstract

A linear multistep method (LMM) with continuous coefficients is considered and directly applied to solve first order initial value problems (IVPs). The continuous method is used to obtain Multiple Finite Difference Methods (MFDMs) (each of order 4) which are combined as simultaneous numerical integrators to provide a direct solution to IVPs over sub-intervals which do not overlap. The region of absolute stability is analyzed and the convergence of the MFDMs is discussed by conveniently representing the MFDMs as a block method and verifying that the block methodis zero-stable and consistent. The superiority of the methods over the two stepadamsmoulton method is established numerically.

Keywords: Block Method; Linear Multistep Method; Multistep Collocation; Continuous Multistep (CM), Zerostability

Journal of the Nigerian Association of Mathematical Physics, Volume 19 (November, 2011), pp 159 – 166