Jacobian reuse in explicit integrators for higher index DAEs

Applied Numerical Mathematics

Volumn 25, Issue 4, 1997, Pages 391-412

  Campbell, Stephen L ^a   Zhong, Yangchun ^a  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

DAE; Differential algebraic equation; Numerical methods

Indexed keywords

COMPUTATIONAL METHODS; INTEGRATION; MATRIX ALGEBRA; NUMERICAL METHODS; PROBLEM SOLVING; VECTORS;

DIFFERENTIAL ALGEBRAIC EQUATIONS; EXPLICIT INTEGRATION METHOD; JACOBIAN REUSE;

DIFFERENTIAL EQUATIONS;

EID: 0031373240     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(97)00052-4     Document Type: Article

References (25)

1. A. Ben-Israel, A modified Newton-Raphson method for the solution of systems of equations, Israel J. Math. 3 (1965) 94-98.
2. A. Ben-Israel, A Newton-Raphson method for the solution of systems of equations, J. Math. Anal. Appl. 15 (1966) 243-252.
3. K.E. Brenan, Numerical simulation of trajectory prescribed path control problems by backward differentiation formulas, IEEE Trans. Automat. Control 31 (1986) 266-269.
4. K.E. Brenan, S.L. Campbell and L.R. Petzold, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations (SIAM, Philadelphia, PA, 1996).
5. S.L. Campbell, A computational method for general higher index singular systems of differential equations, in: MACS Trans. Sci. Comput. '89 1.2 (Baltzer, Basel, 1989) 555-560.
6. S.L. Campbell, Least squares completions for nonlinear differential algebraic equations, Numer. Math. 65 (1993) 77-94.
7. S.L. Campbell, High index differential algebraic equations, J. Mech. Struct. Mach. 23 (1994) 199-222.
8. S.L. Campbell and C.W. Gear, The index of general nonlinear DAEs, Numer. Math. 72 (1995) 173-196.
9. S.L. Campbell and E. Griepentrog, Solvability of general differential algebraic equations, SIAM J. Sci. Statist. Comput. 16 (1995) 257-270.
10. S.L. Campbell and R. Hollenbeck, Automatic differentiation and implicit differential equations, in: M. Berz, C. Bischof, G. Corliss and A. Griewank, eds., Computational Differentiation: Techniques, Applications, and Tools (SIAM, Philadelphia, PA, 1996) 215-227.
11. S.L. Campbell, C.T. Kelley and K.D. Yeomans, Consistent initial conditions for unstructured higher index DAEs: a computational study, in: Proceedings Computational Engineering in Systems Applications, Lille, France (1996) 416-421.
12. S.L. Campbell and W. Marszalek, DAEs arising from traveling wave solutions of PDEs, Mathematical Modelling of Systems, to appear.
13. S.L. Campbell and C.D. Meyer Jr, Generalized Inverses of Linear Transformations (Dover Press, New York, 1991).
14. S.L. Campbell and E. Moore, Progress on a general numerical method for nonlinear higher index DAEs II, Circuits Systems Signal Process. 13 (1994) 123-138.
15. S.L. Campbell and E. Moore, Constraint preserving integrator for general nonlinear higher index DAEs, Numer. Math. 69 (1995) 383-399.
16. S.L. Campbell, E. Moore and Y. Zhong, Utilization of automatic differentiation in control algorithms, IEEE Trans. Automat. Control 39 (1994) 1047-1052.
17. S.L. Campbell, E. Moore and Y. Zhong, Constraint preserving integrators for unstructured higher index DAEs, Z. Angew. Math. Mech. 76 (1996) 83-86.
18. T.F. Chan, Rank revealing QR factorizations, Linear Algebra Appl. 88/89 (1987) 67-82.
19. A. De Luca and A. Isidori, Feedback linearization of invertible systems, in: Proceedings Colloquium on Automation and Robots, Duisberg (1987).
20. E. Hairer, C. Lubich and M. Roche, The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods (Springer, New York, 1989).
21. J.B. Keiper and C.W. Gear, The analysis of generalized backward difference formula methods applied to Hessenberg form differential-algebraic equations, SIAM J. Numer. Anal. 28 (1991) 833-858.
22. C. Majer, W. Marquardt and E.D. Gilles, Reinitialization of DAE's after discontinuities, in: ESCAPE '95, to appear.
23. D. von Wissel, R. Nikoukhah, S.L. Campbell and F. Delebecque, Nonlinear observer design using implicit system descriptions, in: Proceedings Computational Engineering in Systems Applications, Lille, France (1996) 404-409.
24. J. Unger, A. Kröner and W. Marquardt, Structural analysis of differential-algebraic equation systems -theory and application, Comput. Chem. Engrg. 19 (1995) 867-882.
25. Y. Zhong, Efficient numerical solutions of general nonlinear higher index differential algebraic equations, Ph.D. Thesis, North Carolina State University, Raleigh, NC (1997).