Download or read book Nonlinear Asymptotic Integration Algorithms for One-Dimensional Autonomous Dissipative First-Order Odes written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-08-20 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear asymptotic integrators are applied to one-dimensional, nonlinear, autonomous, dissipative, ordinary differential equations. These integrators, including a one-step explicit, a one-step implicit, and a one- and two-step midpoint algorithm, are designed to follow the asymptotic behavior of a system approaching a steady state. The methods require that the differential equation be written in a particular asymptotic form. This is always possible for a one-dimensional equation with a globally asymptotic steady state. In this case, conditions are obtained to guarantee that the implicit algorithms are well defined. Further conditions are determined for the implicit methods to be contractive. These methods are all first order accurate, while under certain conditions the midpoint algorithms may also become second order accurate. The stability of each method is investigated and an estimate of the local error is provided. Haslach, Henry W., Jr. and Freed, Alan D. and Walker, Kevin P. Glenn Research Center NAG3-1321; RTOP 505-63-5A...