Two perspectives on reduction of ordinary differential equations

DOI10.1002/mana.200410328zbMath1085.34036OpenAlexW2154882140MaRDI QIDQ5711814

Hans G. Kaper, Tasso J. Kaper, Antonios Zagaris

Publication date: 8 December 2005

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.200410328

zbMATH Keywords

dimension reductionnormal formkinetic equationsslow manifoldmultiple time scalesNonlinear differential equationscomputational singular perturbationzero derivative principle

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) (92C45) Combustion (80A25) Chemical kinetics in thermodynamics and heat transfer (80A30) Singular perturbations for ordinary differential equations (34E15) Multiple scale methods for ordinary differential equations (34E13)

Related Items (15)

On Differential Geometric Formulations of Slow Invariant Manifold Computation: Geodesic Stretching and Flow Curvature ⋮ Algorithmic asymptotic analysis of the NF-\(\kappa\mathrm B\) signaling system ⋮ Geometry of the Computational Singular Perturbation Method ⋮ Stretching-based diagnostics and reduction of chemical kinetic models with diffusion ⋮ Glycolysis in saccharomyces cerevisiae: algorithmic exploration of robustness and origin of oscillations ⋮ Quasi steady state and partial equilibrium approximations: their relation and their validity ⋮ Classical quasi-steady state reduction -- a mathematical characterization ⋮ Single-soliton solution of KdV equation via Hirota's direct method under the time scale framework ⋮ Algorithmic criteria for the validity of quasi-steady state and partial equilibrium models: the Michaelis-Menten reaction mechanism ⋮ Hunting French ducks in a noisy environment ⋮ Computational Singular Perturbation Method for Nonstandard Slow-Fast Systems ⋮ The role of slow system dynamics in predicting the degeneracy of slow invariant manifolds: the case of vdP relaxation-oscillations ⋮ Physical understanding of complex multiscale biochemical models via algorithmic simplification: glycolysis in saccharomyces cerevisiae ⋮ Three-dimensional direct numerical simulation of a turbulent lifted hydrogen jet flame in heated coflow: a chemical explosive mode analysis ⋮ The ``hidden dynamics of the Rössler attractor

Cites Work

• Unnamed Item
• Unnamed Item
• Constraint-defined manifolds: a legacy code approach to low-dimensional computation
• Equation-free, coarse-grained multiscale computation: enabling microscopic simulators to perform system-level analysis
• Projecting to a Slow Manifold: Singularly Perturbed Systems and Legacy Codes

This page was built for publication: Two perspectives on reduction of ordinary differential equations