Semiexplicit -stable Runge-Kutta methods

Authors:
G. J. Cooper and A. Sayfy

Journal:
Math. Comp. **33** (1979), 541-556

MSC:
Primary 65L05

DOI:
https://doi.org/10.1090/S0025-5718-1979-0521275-1

MathSciNet review:
521275

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Abstract: An stage semiexplicit Runge-Kutta method is represented by an real lower triangular matrix where the number of implicit stages is given by the number of nonzero diagonal elements. It is shown that the maximum order attainable is *s* when . Necessary and sufficient conditions for *A*-stability are derived and it is shown that there must be implicit stages if the order is *s* and . Examples are given for where all the nonzero diagonal elements are equal. Additional problems arise when ; but when , an *A*-stable method of order 5 is obtained. This method has five nonzero diagonal elements, and these elements are equal. Finally, a six stage *A*-stable method of order six is given. Again, this method has five nonzero (and equal) diagonal elements.

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DOI:
https://doi.org/10.1090/S0025-5718-1979-0521275-1

Article copyright:
© Copyright 1979
American Mathematical Society