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Recent advances in stiff ODE solvers. (English) Zbl 0707.65044

Computational mathematics II, Proc. 2nd Int. Conf. Numer. Anal. Appl., Benin City/Niger. 1986, Conf. Ser., Boole Press 11, 21-32 (1987).
[For the entire collection see Zbl 0655.00016.]
This paper presents a brief survey of some of the codes and underlying methods and techniques developed for solving stiff ordinary differential equations. Topics covered include BDF methods (Gear, Hindmarsh), extrapolation processes (Lindberg, Bader and Deuflhard), the Enright- Hessenberg technique, second derivative methods (Enright, Addison), diagonally implicit Runge-Kutta methods (Alexander, Nørsett) and singly implicit methods (the reviewer).
Reviewer: K.Burrage

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis

Citations:

Zbl 0655.00016