Open Access
Original Articles
Numerical Treatment of Differential-Algebraic Equations with Index 2 by Reducing the Index
Basem Attilib.attili@sharjah.ac.aeUniversity of SharjahMathematics Department, Sharjah, P. O. Box 27272View full profile → , Alaa Abu-HatabMathematical Sciences Department Al-AinUnited Arab Emirates UniversityP. O. Box 17551, United Arab EmiratesView full profile → , Aseel AyoubMathematical Sciences Department Al-AinUnited Arab Emirates UniversityP. O. Box 17551, United Arab EmiratesView full profile → , Ayat IsmailMathematical Sciences Department Al-AinUnited Arab Emirates UniversityP. O. Box 17551, United Arab EmiratesView full profile → , Shefa Abu-GhneimMathematical Sciences Department Al-AinUnited Arab Emirates UniversityP. O. Box 17551, United Arab EmiratesView full profile →
* Corresponding author · click or hover a name for details
- Published Online:
- 03 Jun 2013
- Article type:
- Original Articles
- Language:
- EN
- Article no.:
- 1726037X.2008.10698544
- Pages:
- 49–60
Abstract
We will consider the solution of Hessenberg index-2 differential algebraic equations(DAE) numerically. We first introduce a method to reduce the index from 2 to index 1 resulting in an easier problem to solve. For the numerical treatment, we will use power series solutions coupled with pade’ approximation for better convergence results. Numerical examples will be presented also.
Subject Classifications
: Index-2 Differential Algebraic SystemsIndex reductionPower series
References
- Attili, B. S.2006 . Continuation Method for Computing Certain Singular Points for Index-1 Differential Algebraic Equations . , 175 : 1026 – 1038 .
- Attili, B. S.2006 . Arclength Continuation With Finite Difference Method for Computing Cups Points of Differential-Algebraic Equations with Index-1 . , 8 : 47 – 59 .
- Ayaz, F.2004 . Applications of Differential Transform Method to Differential-Algebraic Equations . , 152 : 649 – 657 .
- Babolian, E. and Hosseini, M. M.2003 . Reducing index and pseudospectral methods for differential-algebraic equations . , 140 : 77 – 90 .
- Brenan, K. E., Campbell, S. L. and Petzold, L. R.1989 . , Amsterdam: Elsevier .
- Burden, R. and Faires, J.2001 . , 7th , Books/cole .
- Celik, E. and Bayram, M.2005 . The Numerical Solution of Physical Problems Modeled as a System of Differential-Algebraic Equations (DAEs) . , 342 : 1 – 6 .
- Celik, E. and Bayram, M.2004 . Numerical Solution of Differential-Algebraic Equation Systems and Applications . , 154 : 405 – 413 .
- Celik, E.2004 . Numerical Solution of Differential-Algebraic Equations With Index-2 . , 156 : 541 – 550 .
- Gorbuov, V. K. and Lutoshkin, I. V.2006 . The Parameterization Method in Optimal Control Problems and Differential-Algebraic Equations . , 185 : 377 – 390 .
- Hosseini, M. M.2005 . Numerical Solution of Linear Differential-Algebraic Equations . , 162 : 7 – 14 .
- Ren, Y. and Spence, A.1999 . A note on Bifurcation Points for Index-1 Differential-Algebraic Problems . , 110 : 1 – 14 .
- Schropp, J.2003 . Attracting Sets in Index 2 Differential Algebraic Equations and in Their Runge-Kutta Discretization . , 52 : 1185 – 1197 .
- Sun, W. and Jiang, Y-L.2005 . Runge-Kutta Methods of Dynamic Iteration for Index-2 Differential-Algebraic Equations . , 169 : 1346 – 1363 .
- Vijalapura, P. K., Strain, J. and Govindjee, S.2005 . Fractional Step Method for Index-1 Differential-Algebraic Equations . , 203 : 305 – 320 .
Views: 44Downloads: 72Citations: 1
