A Fifth Order Hybrid Linear Multistep method For the Direct Solution Of ym = f (x, y)

Abstract

A linear multistep hybrid method (LMHM)with continuous coefficients isconsidered and directly applied to solve third order initial and boundary value problems (IBVPs). 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 convenientlyrepresenting theMFDMs as a block method and verifying that the block method is zero-stable and consistent. The superiority of the MFDMs over the methods in Olabode and Yusuph [12] is established numerically.

Keywords: Multiple finite difference methods, third order, boundary value problem, block methods, multistep methods

Journal of the Nigerian Association of Mathematical Physics, Volume 19 (November, 2011), pp 167 - 174