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The order ofB-convergence of algebraically stable Runge-Kutta methods (1987)

Burrage, K. ; Hundsdorfer, W. H.

Springer

BIT 27 (1987), S. 62-71

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ISSN: 1572-9125

Keywords: 65L05 ; Numerical analysis ; stiff initial value problems ; implicit Runge-Kutta methods ; B-convergence

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract In a previous paper it was shown that for a class of semi-linear problems many high order Runge-Kutta methods have order of optimalB-convergence one higher than the stage order. In this paper we show that for the more general class of nonlinear dissipative problems such as result holds only for a small class of Runge-Kutta methods and that such methods have at most classical order 3.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01937355

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