Development of Implicit Hybrid Adams Type Block Linear Multistep Method for the Solution of Stiff Ordinary Differential Equations

Abstract

This paper proposes the derivation of a three-step eleventh order hybrid linear multi-step method (LMM) with nine off-step points for the solution of first order stiff differential equations. The obtained methods are then applied in block form as simultaneous numerical integrators over non-overlapping intervals. The numerical results show improved results over the existing methods in literatures considered, the schemes are consistent, zero-stable, and convergent.