Comparative analysis of integration methods for nonlinear elasticity theory equations}  / M. V. Kozlov, S. V. Sheshenin. //Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2013. ? 4. P. 61-65 [Moscow Univ. Math. Bulletin. Vol. 68, N 4, 2013.].

In this paper we describe the way of practical solution of the variational equation in geometrically and physically nonlinear problems of deformable body mechanics. A system of a large number of nonlinear ordinary differential equations usually appears in such problems. The Euler method is typically used in this approach. We propose to use a Runge-Kutta method and multistep methods and consider the solution complexity in terms of computing cost to find a method that provides a more efficient solving procedure of nonlinear problems.

Key words: rubber-cord, composite, nonlinearity, variational equation, linearization, finite element method, Euler method, Newton method, Runge-Kutta method, multistep method.