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A convergence criterion for a class of integration methods


Author: J. C. Butcher
Journal: Math. Comp. 26 (1972), 107-117
MSC: Primary 65L99
DOI: https://doi.org/10.1090/S0025-5718-1972-0305609-2
MathSciNet review: 0305609
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Abstract: A criterion is established for the convergence of sequences of a general type of Runge-Kutta method. The criterion is expressed in terms of ``weak convergence", a property defined in the paper.


References [Enhancements On Off] (What's this?)

  • [1] G. Dahlquist, ``Convergence and stability in the numerical integration of ordinary differential equations,'' Math. Scand., v. 4, 1956, pp. 33-53. MR 18, 338. MR 0080998 (18:338d)
  • [2] P. Henrici, Discrete Variable Methods in Ordinary Differential Equations, Wiley, New York, 1962. MR 24 #B1772. MR 0135729 (24:B1772)
  • [3] J. C. Butcher, ``On the convergence of numerical solutions to ordinary differential equations,'' Math. Comp., v. 20, 1966, pp. 1-10. MR 32 #6678. MR 0189251 (32:6678)
  • [4] J. C. Butcher, ``An algebraic theory of integration methods,'' Math. Comp., v. 26, 1972, pp. 79-106. MR 0305608 (46:4738)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1972-0305609-2
Keywords: Runge-Kutta methods, initial value problems, convergence
Article copyright: © Copyright 1972 American Mathematical Society

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