The application of implicit RungeKutta and collection methods to boundaryvalue problems
Author:
Richard Weiss
Journal:
Math. Comp. 28 (1974), 449464
MSC:
Primary 65L10
MathSciNet review:
0341881
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Abstract: The solution of a nonlinear system of first order differential equations with nonlinear boundary conditions by implicit RungeKutta methods based on interpolatory quadrature formulae is examined. An equivalence between implicit RungeKutta 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
DOI:
http://dx.doi.org/10.1090/S00255718197403418812
PII:
S 00255718(1974)03418812
Keywords:
Implicit RungeKutta method,
collocation method,
boundaryvalue problem
Article copyright:
© Copyright 1974
American Mathematical Society
