A comparative analysis of methods for solving equations in the nonlinear elasticity theory

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.