Weakly corrected numerical solutions to stochastically driven nonlinear dynamical systems

Sarkar, Saikat and Roy, Debasish (2016) Weakly corrected numerical solutions to stochastically driven nonlinear dynamical systems. In: APPLIED MATHEMATICAL MODELLING, 40 (2). pp. 859-870.

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Abstract

A method to weakly correct the solutions of stochastically driven nonlinear dynamical systems, herein numerically approximated through the Eule-Maruyama (EM) time-marching map, is proposed. An essential feature of the method is a change of measures that aims at rendering the EM-approximated solution measurable with respect to the filtration generated by an appropriately defined error process. Using Ito's formula and adopting a Monte Carlo (MC) setup, it is shown that the correction term may be additively applied to the realizations of the numerically integrated trajectories. Numerical evidence, presently gathered via applications of the proposed method to a few nonlinear mechanical oscillators and a semi-discrete form of a 1-D Burger's equation, lends credence to the remarkably improved numerical accuracy of the corrected solutions even with relatively large time step sizes. (C) 2015 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Publication:	APPLIED MATHEMATICAL MODELLING
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:	Nonlinear stochastic dynamical systems; Euler-Maruyama method; Integration error; Weak correction; Change of measures
Department/Centre:	Division of Mechanical Sciences > Civil Engineering
Date Deposited:	29 Jan 2016 06:09
Last Modified:	29 Jan 2016 06:09
URI:	http://eprints.iisc.ac.in/id/eprint/53166

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