Formal series and numerical integrators, part II: Application to index-2 differential-algebraic systems

Applied Numerical Mathematics

Volumn 29, Issue 1, 1999, Pages 99-113

  Murua, A ^a  

^a UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; ESTIMATION; INTEGRATION; RUNGE KUTTA METHODS;

DIFFERENTIAL ALGEBRAIC EQUATION; FORMAL SERIES; HAMILTONIAN SYSTEMS;

CONVERGENCE OF NUMERICAL METHODS;

EID: 0032714026     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(98)00070-1     Document Type: Article

References (13)

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2. A. Aubry and P. Chartier, On the structure of errors for Radau IA methods applied to index-2 DAEs, Appl. Numer. Math. 22 (1996) 23-34.
3. V. Brasey and E. Hairer, Half-explicit Runge-Kutta methods for differential-algebraic systems of index 2, SIAM J. Numer. Anal. 30 (1993) 538-552.
4. K.E. Brenan, S.L. Campbell and L.R. Petzold, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations (North-Holland, New York, 1989).
5. R.P.K. Chan and P. Chartier, A composition law for Runge-Kutta methods applied to index-2 differential-algebraic equations, BIT 36 (1996) 229-246.
6. E. Hairer, Ch. Lubich and M. Roche, The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods, Lecture Notes in Mathematics 1409 (Springer, New York, 1989).
7. E. Hairer, S.P. Nørsett and G. Wanner, Solving Ordinary Differential Equations I. Non-Stiff Problems, 2nd ed. (Springer, New York, 1993).
8. E. Hairer and G. Wanner, Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems, 2nd ed. (Springer, New York, 1996).
9. L. Jay, Convergence of a class of Runge-Kutta methods for differential-algebraic systems of index 2, BIT 33 (1993) 137-150.
10. L. Jay, Runge-Kutta methods for differential-algebraic systems of index 3 with applications to Hamiltonian systems, Ph.D. Thesis, Univ. de Genève (1994).
11. A. Murua, Partitioned Runge-Kutta methods for semi-explicit differential-algebraic systems of index 2, Technical Report EHU-KZAA-IKT-196 (1996).
12. A. Murua, Partitioned half-explicit Runge-Kutta methods for differential-algebraic systems of index 2, Computing 59 (1997) 43-61.
13. A. Murua, Formal series and numerical integrators, Part I: Systems of ODEs and symplectic integrators, Appl. Numer. Math. 29 (2) (1999) 221-251.