2007/09/28 by Michael Robinson, Robinson, Michael · 3 citations
Computer Science · Mathematics · #Matrix Theory and Algorithms #Numerical methods for differential equations #Polynomial and algebraic computation #math.CA #msc:34B40 #msc:34E05
paper · pdf · doi:10.48550/arxiv.0709.4664
30 pages, 12 figures
arxiv created 2007/09/28 · arxiv updated 2009/12/01
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.