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.
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April 2011
Research Papers
Unified Galerkin- and DAE-Based Approximation of Fractional Order Systems
Satwinder Jit Singh,
Satwinder Jit Singh
Mechanical Engineering,
e-mail: sjitsingh@rediffmail.com
Indian Institute of Science
, Bangalore 560012, India
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Anindya Chatterjee
Anindya Chatterjee
Mechanical Engineering,
e-mail: anindya100@gmail.com
Indian Institute of Science
, Bangalore 560012, India
Search for other works by this author on:
Satwinder Jit Singh
Mechanical Engineering,
Indian Institute of Science
, Bangalore 560012, Indiae-mail: sjitsingh@rediffmail.com
Anindya Chatterjee
Mechanical Engineering,
Indian Institute of Science
, Bangalore 560012, Indiae-mail: anindya100@gmail.com
J. Comput. Nonlinear Dynam. Apr 2011, 6(2): 021010 (7 pages)
Published Online: October 28, 2010
Article history
Received:
September 15, 2009
Revised:
August 18, 2010
Online:
October 28, 2010
Published:
October 28, 2010
Citation
Singh, S. J., and Chatterjee, A. (October 28, 2010). "Unified Galerkin- and DAE-Based Approximation of Fractional Order Systems." ASME. J. Comput. Nonlinear Dynam. April 2011; 6(2): 021010. https://doi.org/10.1115/1.4002516
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