The time finite element as a robust general scheme for solving nonlinear dynamic equations including chaotic systems

Jog, CS and Agrawal, Manish and Nandy, Arup (2016) The time finite element as a robust general scheme for solving nonlinear dynamic equations including chaotic systems. In: APPLIED MATHEMATICS AND COMPUTATION, 279 . pp. 43-61.

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Abstract

Schemes that can be proven to be unconditionally stable in the linear context can yield unstable solutions when used to solve nonlinear dynamical problems. Hence, the formulation of numerical strategies for nonlinear dynamical problems can be particularly challenging. In this work, we show that time finite element methods because of their inherent energy momentum conserving property (in the case of linear and nonlinear elastodynamics), provide a robust time-stepping method for nonlinear dynamic equations (including chaotic systems). We also show that most of the existing schemes that are known to be robust for parabolic or hyperbolic problems can be derived within the time finite element framework; thus, the time finite element provides a unification of time-stepping schemes used in diverse disciplines. We demonstrate the robust performance of the time finite element method on several challenging examples from the literature where the solution behavior is known to be chaotic. (C) 2015 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Publication:	APPLIED MATHEMATICS AND COMPUTATION
Publisher:	ELSEVIER SCIENCE INC
Additional Information:	Copy right for this article belongs to the ELSEVIER SCIENCE INC, 360 PARK AVE SOUTH, NEW YORK, NY 10010-1710 USA
Keywords:	Time finite element method; Chaotic system; Nonlinear dynamics
Department/Centre:	Division of Mechanical Sciences > Mechanical Engineering
Date Deposited:	31 Mar 2016 04:05
Last Modified:	31 Mar 2016 04:05
URI:	http://eprints.iisc.ac.in/id/eprint/53436

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