An efficient numerical method for solving dynamical systems with multiple time scales

DOI10.3934/cac.2024013MaRDI QIDQ6616140

Zhiwen Zhang, Zhongjian Wang

Publication date: 8 October 2024

Published in: Communications on Analysis and Computation (Search for Journal in Brave)

zbMATH Keywords

convergence analysisstiff equationsmultiple time scalesHamiltonian dynamical systemcomposite maps

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Multiple scale methods for ordinary differential equations (34E13) Numerical methods for stiff equations (65L04)

Cites Work

• Multiple time scale dynamics
• Nonlinear approximation via compositions
• Uniformly accurate numerical schemes for highly oscillatory Klein-Gordon and nonlinear Schrödinger equations
• Equation-free, coarse-grained multiscale computation: enabling microscopic simulators to perform system-level analysis
• Nonintrusive and Structure Preserving Multiscale Integration of Stiff ODEs, SDEs, and Hamiltonian Systems with Hidden Slow Dynamics via Flow Averaging
• The heterogeneous multiscale method
• Multiscale Finite Element Methods
• The Hénon and Heiles Problem in Three Dimensions.
• Heterogeneous multiscale methods for stiff ordinary differential equations
• Geometric Numerical Integration

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