An asymptotic-numerical approach for examining global solutions to an ordinary differential equation

Details An asymptotic-numerical approach for examining global solutions to an ordinary differential equation An asymptotic-numerical approach for examining global solutions to an ordinary differential equation

2007-09-28

arxiv.org/abs/0709.4664v1

Mathematics

Classical Analysis and ODEs

30 pages, 12 figures

Scientific paper

Purely numerical methods do not always provide an accurate way to find all the global solutions to nonlinear ODE on infinite intervals. For example, finite-difference methods fail to capture the asymptotic behavior of solutions, which might be critical for ensuring global existence. We first show, by way of a detailed example, how asymptotic information alone provides significant insight into the structure of global solutions to a nonlinear ODE. Then we propose a method for providing this missing asymptotic data to a numerical solver, and show how the combined approach provides more detailed results than either method alone.

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