A New Non-linear Multistep Method Based on Centroidal Mean in Solving Initial Value Problems

Abstract

A new 2-step fourth order implicit non-linear multistep method based on centroidal mean is considered in this paper. The new method is tested on some test problems; and numerical results show that the new method is able to produce acceptable numerical solutions for these test problems. Comparisons in terms of numerical accuracy between the new method and the classical 2-step Adams-Moulton method are carried out as well. Numerical experiments show that our new method performs better than the classical 2-step Adams-Moulton method in solving these test problems. Keywords: Initial value problems; non-linear multistep method; centroidal mean; Adams-Moulton method; 3-stage fourth order Lobatto IIIC method