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Asymptotic integration algorithms for nonhomogeneous, nonlinear, first order, ordinary differential equationsNew methods for integrating systems of stiff, nonlinear, first order, ordinary differential equations are developed by casting the differential equations into integral form. Nonlinear recursive relations are obtained that allow the solution to a system of equations at time t plus delta t to be obtained in terms of the solution at time t in explicit and implicit forms. Examples of accuracy obtained with the new technique are given by considering systems of nonlinear, first order equations which arise in the study of unified models of viscoplastic behaviors, the spread of the AIDS virus, and predator-prey populations. In general, the new implicit algorithm is unconditionally stable, and has a Jacobian of smaller dimension than that which is acquired by current implicit methods, such as the Euler backward difference algorithm; yet, it gives superior accuracy. The asymptotic explicit and implicit algorithms are suitable for solutions that are of the growing and decaying exponential kinds, respectively, whilst the implicit Euler-Maclaurin algorithm is superior when the solution oscillates, i.e., when there are regions in which both growing and decaying exponential solutions exist.
Document ID
19910012484
Acquisition Source
Legacy CDMS
Document Type
Technical Memorandum (TM)
Authors
Walker, K. P.
(Engineering Science Software, Inc., Smithfield RI., United States)
Freed, A. D.
(NASA Lewis Research Center Cleveland, OH, United States)
Date Acquired
September 6, 2013
Publication Date
March 1, 1991
Subject Category
Numerical Analysis
Report/Patent Number
NASA-TM-103793
NAS 1.15:103793
E-6070
Accession Number
91N21797
Funding Number(s)
PROJECT: RTOP 553-13-00
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.
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