Geodesic
A comparative analysis of methods for solving equations in the nonlinear elasticity theory
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2013), pp. 61-65

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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. 
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     author = {M. V. Kozlov and S. V. Sheshenin},
     title = {A comparative analysis of methods for solving equations in the nonlinear elasticity theory},
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M. V. Kozlov; S. V. Sheshenin. A comparative analysis of methods for solving equations in the nonlinear elasticity theory. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2013), pp. 61-65. http://geodesic.mathdoc.fr/item/VMUMM_2013_4_a13/