Applicability of the homotopy method to the determination of fixed points in chemical kinetics models

DOI10.1016/S0096-3003(98)10116-9zbMath1023.65073OpenAlexW2093974213MaRDI QIDQ1569172

H. Labro, B. Maheu, Annie Garo

Publication date: 25 June 2000

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0096-3003(98)10116-9

zbMATH Keywords

comparison of methodsstability analysisfixed pointhomotopy methodBelousov-Zhabotinskii reactionnonlinear dynamical systemquasi-steady-state assumptionreduction schemeschemical kinetics systemNewton-Raphson algorithmsturbulent combusting

Mathematics Subject Classification ID

Classical flows, reactions, etc. in chemistry (92E20) Nonlinear ordinary differential equations and systems (34A34) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Structural stability and analogous concepts of solutions to ordinary differential equations (34D30) Numerical investigation of stability of solutions to ordinary differential equations (65L07) Chemical kinetics in thermodynamics and heat transfer (80A30) Generic properties, structural stability of dynamical systems (37C20) Numerical nonlinear stabilities in dynamical systems (65P40)

Cites Work

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• A globally convergent algorithm for computing fixed points of \(C^2\) maps
• Homoclinic chaos in chemical systems
• Algorithm 652
• Finding Zeroes of Maps: Homotopy Methods That are Constructive With Probability One
• Finding all isolated solutions to polynomial systems using HOMPACK

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