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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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The application of implicit Runge-Kutta and collection methods to boundary-value problems
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by Richard Weiss PDF
Math. Comp. 28 (1974), 449-464 Request permission

Abstract:

The solution of a nonlinear system of first order differential equations with nonlinear boundary conditions by implicit Runge-Kutta methods based on interpolatory quadrature formulae is examined. An equivalence between implicit Runge-Kutta and collocation schemes is established. It is shown that the difference equations obtained have a unique solution in a neighbourhood of an isolated solution of the continuous problem, that this solution can be computed by Newton iteration and that it converges to the isolated solution. The order of convergence is equal to the degree of precision of the related quadrature formula plus one. The efficient implementation of the methods is discussed and numerical examples are given.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Math. Comp. 28 (1974), 449-464
  • MSC: Primary 65L10
  • DOI: https://doi.org/10.1090/S0025-5718-1974-0341881-2
  • MathSciNet review: 0341881