Unified Galerkin- and DAE-Based Approximation of Fractional Order Systems

Singh, Satwinder Jit and Chatterjee, Anindya (2011) Unified Galerkin- and DAE-Based Approximation of Fractional Order Systems. In: Journal of Computational and Nonlinear Dynamics, 6 (2).

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Abstract

We consider numerical solutions of nonlinear multiterm fractional integrodifferential equations, where the order of the highest derivative is fractional and positive but is otherwise arbitrary. Here, we extend and unify our previous work, where a Galerkin method was developed for efficiently approximating fractional order operators and where elements of the present differential algebraic equation (DAE) formulation were introduced. The DAE system developed here for arbitrary orders of the fractional derivative includes an added block of equations for each fractional order operator, as well as forcing terms arising from nonzero initial conditions. We motivate and explain the structure of the DAE in detail. We explain how nonzero initial conditions should be incorporated within the approximation. We point out that our approach approximates the system and not a specific solution. Consequently, some questions not easily accessible to solvers of initial value problems, such as stability analyses, can be tackled using our approach. Numerical examples show excellent accuracy. DOI: 10.1115/1.4002516]

Item Type:	Journal Article
Publication:	Journal of Computational and Nonlinear Dynamics
Publisher:	The American Society of Mechanical Engineers
Additional Information:	Copyright of this article belongs to The American Society of Mechanical Engineers.
Department/Centre:	Division of Mechanical Sciences > Mechanical Engineering
Date Deposited:	03 Jan 2011 06:41
Last Modified:	03 Jan 2011 06:41
URI:	http://eprints.iisc.ac.in/id/eprint/34760

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