Implementing a seventh-order linear multistep method in a predictor-corrector mode or block mode: which is more efficient for the general second order initial value problem

Abstract

Abstract: A Seventh-Order Linear Multistep Method (SOLMM) is developed and implemented in both predictor-corrector mode and block mode. The two approaches are compared by measuring their total number of function evaluations and CPU times. The stability property of the method is examined. This SOLMM is also compared with existing methods in the literature using standard numerical examples.