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- W2132175179 abstract "The occurrence of logarithmic switchback is studied for ordinary differential equations containing a parameter k which is allowed to take any value in a continuum of real numbers and with boundary conditions imposed at $x = varepsilon $ and $x = infty $. Classical theory tells us that if the equation has a regular singular point at the origin there is a family of solutions which varies continuously with k, and the expansion around the origin has log x terms for a discrete set of values of k. It is shown here how nonlinearity enlarges this set so that it may even be dense in some interval of the real numbers. A $log x$ term in the expansion in x leads to expansion coefficients containing $logvarepsilon $ (switchback) in the perturbation expansion. If for a given value of k logarithmic terms in x and $varepsilon $ occur they may be obtained by continuity from neighboring values of k. Switchback terms occurred conspicuously in singular-perturbation solutions of problems posed for semi-infinite domain $xgeqq varepsilon $. This connection is historical rather than logical. In particular we study here switchback terms for a specific example using methods of both singular and regular perturbations." @default.
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- W2132175179 date "1984-06-01" @default.
- W2132175179 modified "2023-09-27" @default.
- W2132175179 title "Note on Logarithmic Switchback Terms in Regular and Singular Perturbation Expansions" @default.
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- W2132175179 doi "https://doi.org/10.1137/0144030" @default.
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