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The accurate numerical solution of highly oscillatory ordinary differential equations


Author: Robert E. Scheid
Journal: Math. Comp. 41 (1983), 487-509
MSC: Primary 65L05; Secondary 34C29
DOI: https://doi.org/10.1090/S0025-5718-1983-0717698-9
MathSciNet review: 717698
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Abstract: An asymptotic theory for weakly nonlinear, highly oscillatory systems of ordinary differential equations leads to methods which are suitable for accurate computation with large time steps. The theory is developed for systems of the form

\begin{displaymath}\begin{array}{*{20}{c}} {{\mathbf{Z}}'= (A(t)/\varepsilon ){\... ...,\quad 0 < t < T,0 < \varepsilon \ll 1,} \hfill \\ \end{array} \end{displaymath}

where the diagonal matrix $ A(t)$ has smooth, purely imaginary eigenvalues and the components of $ {\mathbf{H}}({\mathbf{Z}},t)$ are polynomial in the components of Z with smooth t-dependent coefficients. Computational examples are presented.

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1983-0717698-9
Keywords: Oscillatory, numerical solution of ordinary differential equations, stiff equations
Article copyright: © Copyright 1983 American Mathematical Society

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