On the efficient implementation of implicit Runge-Kutta methods

Varah, J. M.

doi:10.1090/S0025-5718-1979-0521276-3

On the efficient implementation of implicit Runge-Kutta methods
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Math. Comp. 33 (1979), 557-561 Request permission

Abstract:

Extending some recent ideas of Butcher, we show how one can efficiently implement general implicit Runge-Kutta methods, including those based on Gaussian quadrature formulas which are particularly useful for stiff equations. With this implementation, it appears that these methods are more efficient than the recently proposed semiexplicit methods and their variants.

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