## ARK methods for stiff problems.(English)Zbl 1070.65059

The authors show that it is possible to generalize the almost Runge-Kutta (ARK)methods to stiff problems by adding a constant diagonal to the coefficient matrix $$A$$.

### MSC:

 65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations 65L05 Numerical methods for initial value problems involving ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems

### Keywords:

almost Runge-Kutta methods; Stiff problems; A-stability
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### References:

 [1] Butcher, J.C., An introduction to “almost runge – kutta” methods, Appl. numer. math., 24, 331-342, (1997) · Zbl 0905.65085 [2] Butcher, J.C., ARK methods up to order five, Numer. algorithms, 17, 193-221, (1998) · Zbl 0907.65069 [3] Butcher, J.C., Numerical methods for ordinary differential equations, (2003), Wiley Chichester · Zbl 1032.65512 [4] Butcher, J.C.; Moir, N., Experiments with a new fifth order method, Numer. algorithms, 33, 137-151, (2003) · Zbl 1030.65081 [5] W. Wright, General Linear Methods with Inherent Runge-Kutta Stability, Ph.D. Thesis, Department of Mathematics, The University of Auckland, 2002 · Zbl 1016.65049
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