Derivation of Block Hybrid Method for the Solution of First Order Initial Value Problems in ODEs

Abstract

This paper is concerned with the derivation and implementation of hybrid linear multistep method (LMM) for solving first order differential equations. The continuous and discrete schemes for k=4 with one off-step point at interpolation were derived, where k is the step number of the method. The continuous hybrid formulations were evaluated at various points to obtain discrete schemes, which were used in block form for parallel or sequential solution of initial value problem (IVP). For acceptability, the schemes so derived in block form were tested for consistence, zero stability and convergence. Also provided are examples of initial value problems solved with the proposed schemes in block form.