A note on the efficient implementation of implicit methods for ODEs

Journal of Computational and Applied Mathematics

Volumn 87, Issue 1, 1997, Pages 1-9

  Amodio, Pierluigi ^a   Brugnano, Luigi ^b  

^a UNIVERSITY OF BARI   (Italy)

^b Dipartimento di Matematica U Dini   (Italy)

Author keywords

Implicit methods for ODEs; Modified newton iteration; Splittings

Indexed keywords

APPROXIMATION THEORY; ITERATIVE METHODS; MATRIX ALGEBRA; NONLINEAR EQUATIONS; PROBLEM SOLVING;

IMPLICIT RUNGE KUTTA SCHEMES; MODIFIED NEWTON ITERATION;

DIFFERENTIAL EQUATIONS;

EID: 0031367176     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(97)00167-2     Document Type: Article

References (8)

1. L. Brugnano, D. Trigiante, Solving Differential Problems by Multistep Initial and Boundary Value Methods, Gordon & Breach, London, 1997.
2. L. Brugnano, D. Trigiante, On the potentiality of sequential and parallel codes based on extended trapezoidal rules (ETRs), Appl. Numer. Math. 25 (1997) 1-16.
3. K. Burrage, A special family of Runge-Kutta methods for solving stiff differential equations, BIT 18 (1978) 22-41.
4. J.C. Butcher, On the implementation of implicit Runge-Kutta methods, BIT 16 (1976) 237-240.
5. E. Hairer, G. Wanner, Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Equations, Springer Series in Computational Mathematics, vol. 14, Springer, Berlin, 1991.
6. P.J. van der Houwen, J.J.B. de Swart, Triangularly implicit iteration methods for ODE-IVP solvers, SIAM J. Sci. Comput. 18 (1997) 41-55.
7. P.J. van der Houwen, J.J.B. de Swart, Parallel linear system solvers for Runge-Kutta methods, Adv. Comput. Math. 7 (1-2) (1997) 157-181.
8. S.P. Nørsett, Runge-Kutta methods with a multiple real eigenvalue only, BIT 16 (1976) 388-393.