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Exponential-fitted methods for integrating stiff systems of ordinary differential equations: Applications to homogeneous gas-phase chemical kineticsConventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.
Document ID
19840023209
Document Type
Conference Paper
Authors
Pratt, D. T. (Seattle Univ. WA, United States)
Date Acquired
August 12, 2013
Publication Date
February 1, 1984
Publication Information
Publication: APL Computational Methods. 1984 JPM Spec. Session
Subject Category
NUMERICAL ANALYSIS
Funding Number(s)
CONTRACT_GRANT: NAG3-227
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.