Numerical integration of stiff ODE's of singular perturbation type

DOI10.1007/BF00962058zbMath0747.65052MaRDI QIDQ1175297

Kaspar Nipp

Publication date: 25 June 1992

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

zbMATH Keywords

trajectorieserror estimatesstiff systemsimplicit Runge-Kutta methodssingularly perturbed systemnerve impulsesmooth invariant attractive manifold

Mathematics Subject Classification ID

Neural biology (92C20) Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Error bounds for numerical methods for ordinary differential equations (65L70) Singular perturbations for ordinary differential equations (34E15) Multiple scale methods for ordinary differential equations (34E13)

Related Items (3)

Extension and justification of quasi-steady-state approximation for reversible bimolecular binding ⋮ Asymptotic analysis of two reduction methods for systems of chemical reactions ⋮ Computation of Saddle-Type Slow Manifolds Using Iterative Methods

Cites Work

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• Invariant manifolds of singularly perturbed ordinary differential equations
• Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations
• Breakdown of Stability in Singularly Perturbed Autonomous Systems I. Orbit Equations
• Breakdown of Stability in Singularly Perturbed Autonomous Systems II. Estimates for the Solutions and Application

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