Second-order accurate projective integrators for multiscale problems

DOI10.1016/j.cam.2006.02.018zbMath1110.65063OpenAlexW2065598719MaRDI QIDQ869546

C. William Gear, Steven L. Lee

Publication date: 8 March 2007

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

Full work available at URL: https://doi.org/10.1016/j.cam.2006.02.018

zbMATH Keywords

stabilityRunge-Kutta methodAdams-Bashforth methodstiff differential systemsstep size selectionexplicit methodsmultiscale problemsteleprojective integration

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

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Uses Software

• RKC
• SUNDIALS

Cites Work

• SUNDIALS
• The heterogeneous multiscale methods
• High order explicit methods for parabolic equations
• RKC: An explicit solver for parabolic PDEs
• Jacobian-free Newton-Krylov methods: a survey of approaches and applications.
• Telescopic projective methods for parabolic differential equations
• The development of Runge-Kutta methods for partial differential equations
• Construction of explicit Runge-Kutta pairs with stiffness detection
• Equation-free, coarse-grained multiscale computation: enabling microscopic simulators to perform system-level analysis
• Analysis of the heterogeneous multiscale method for ordinary differential equations
• Fourth Order Chebyshev Methods with Recurrence Relation
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• The Use of Iterative Linear-Equation Solvers in Codes for Large Systems of Stiff IVP<scp>s</scp> for ODE<scp>s</scp>
• Projective Methods for Stiff Differential Equations: Problems with Gaps in Their Eigenvalue Spectrum
• Explicit Time-Stepping for Stiff ODEs
• Heterogeneous multiscale methods for stiff ordinary differential equations
• Second order Chebyshev methods based on orthogonal polynomials