Numerical multisteps matrix methods for Y″ = f(t, Y)

摘要

In this paper, numerical multistep matrix methods for solving coupled systems of second order differential equations are proposed. These methods permit the simultaneous computation of all the entries of a coupled differential system using algebraic symbolic languages. Error bounds for the discretization error in terms of the data are given. The proposed methods avoid the increase of the computational cost derived from the standard transformation of the differential problem into an extended first order system.