Nonlinear Asymptotic Integration Algorithms for One-Dimensional Autonomous Dissipative First-Order Odes

Released on by National Aeronautics and Space Administration (NASA)
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  • Nonlinear Asymptotic Integration Algorithms for One-Dimensional Autonomous Dissipative First-Order Odes Book Detail

  • Author : National Aeronautics and Space Administration (NASA)
  • Release Date : 2018-08-20
  • Publisher : Createspace Independent Publishing Platform
  • Genre :
  • Pages : 28
  • ISBN 13 : 9781722418267
  • File Size : 45,45 MB
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Nonlinear Asymptotic Integration Algorithms for One-Dimensional Autonomous Dissipative First-Order Odes by National Aeronautics and Space Administration (NASA) PDF Summary

Book Description: 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...

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