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Open Access ·Peer-reviewed·ISSN (Online): 2169-0057·ISSN (Print): 1726-037X
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The Journal of Dynamical Systems and Geometric Theories (JDSGT) is a world leading journal publishing high quality, rigorously peer-reviewed original research on dynamical systems and geometry, including the interactions between these two subjects and interdisciplinary research with other branches of knowledge since 2003. Topics published by the Journal include but are not limited to: Random dynamical systems Geometry and physics Dynamical systems with hyperbolic behaviour Real and complex geometry Ergodic theory Distance geometry Topological dynamics Global differential geometry Infinite-dimensional Hamiltonian systems Symplectic geometry, contact geometry The journal considers original research articles, survey articles, and book reviews for publication. Responses to articles and correspondence will also be considered at the Chief Editor’s discretion.

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Open Access Original Articles

The Differential Transform Method for the Numerical Treatment of Differential-Algebraic Equations with Index 2

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pp. 147–159Vol. 7Issue 2June 2013DOI: 10.1080/1726037X.2009.10698570XML
Published Online:
03 Jun 2013
Article type:
Original Articles
Language:
EN
Article no.:
1726037X.2009.10698570
Pages:
147–159

Abstract

We will consider the numerical solution of the Hessenberg linear index-2 differential algebraic equations (DAE’s) using the differential transform method. We will first present a method to reduce the index of the DAE to index-1. This results in a problem easier to solve. Numerical examples in addition to the comparison with the work of others will also be presented to show the efficiency of the method.

Keywords

References

Attili, B. S.2006 . Continuation Method for Computing Certain Singular Points for Index-1 Differential Algebraic Equations . Appl. Math, and Comput., 175 : 1026 – 1038 . Attili, B. S.2006 . Arclength Continuation With Finite Difference Method for Computing Cups Points of Differential-Algebraic Equations with Index-1 . CUBO Math. J., 8 : 47 – 59 . Attili, B. S., Abu-Hatab, A., Ayoub, A., Ismail, A. and Abu-Ghneim, Sh.Numerical Treatment of Differential-Algebraic Equations with Index 2 by Reducing the Indexsubmitted. Ayaz, F.2004 . Applications of Differential Transform Method to Differential-Algebraic Equations . Appl. Math. Comp., 152 : 649 – 657 . Babolian, E. and Hosseini, M. M.2003 . Reducing index and pseudospectral methods for differential-algebraic equations . Appli. Math. Comput., 140 : 77 – 90 . Brenan, K. E., Campbell, S. L. and Petzold, L. R.1989 . Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, Amsterdam: Elsevier . Burden, R. and Faires, J.2001 . Numerical Analysis, 7th , Books/cole . Celik, E. and Bayram, M.2005 . The Numerical Solution of Physical Problems Modeled as a System of Differential-Algebraic Equations (DAEs) . J. Frank. Inst., 342 : 1 – 6 . Celik, E. and Bayram, M.2004 . Numerical Solution of Differential-Algebraic Equation Systems and Applications . Appl. Math. Comp., 154 : 405 – 413 . Celik, E.2004 . Numerical Solution of Differential-Algebraic Equations With Index-2 . Appl. Math. Comp., 156 : 541 – 550 . Chen, C. K. and Ho, S. H.1999 . Solving Partial Differential Equations by Two Dimensional Differential Transform Method . Appl. Math. Comput., 106 : 171 – 179 . Chua, L. O. and Deng, An. 1989 . Impasse Points. Part I: Numerical Aspects . Int. J. Circuit Theory Appl., 17 : 213 – 235 . Gorbuov, V. K. and Lutoshkin, I. V.2006 . The Parameterization Method in Optimal Control Problems and Differential-Algebraic Equations . J. Comp. Appl. Math, 185 : 377 – 390 . Hosseini, M. M.2005 . Numerical Solution of Linear Differential-Algebraic Equations . Appl. Math. Comp., 162 : 7 – 14 . Lamour, R., Marz, R. and Winkler, R.1998 . How Floguet Theory Applies to Differential Algebraic equations . J. Math. Anal. Appl., 217 : 372 – 394 . Ren, Y. and Spence, A.1999 . A note on Bifurcation Points for Index-1 Differential-Algebraic Problems . J. Comp. Appl. Math, 110 : 1 – 14 . Schropp, J.2003 . Attracting Sets in Index 2 Differential Algebraic Equations and in Their Runge-Kutta Discretization . Nonlin. Anal., 52 : 1185 – 1197 . Sun, W. and Jiang, Y-L.2005 . Runge-Kutta Methods of Dynamic Iteration for Index-2 Differential-Algebraic Equations . Appl. Math. Comp., 169 : 1346 – 1363 . Vijalapura, P. K., Strain, J. and Govindjee, S.2005 . Fractional Step Method for Index-1 Differential-Algebraic Equations . J. Comp. Phys., 203 : 305 – 320 . Zhou, J. K.1986 . Differential Transformation and its Application for Electrical circuits, Wuhan: Huazhong University Press .
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