Exponential-Krylov methods for ordinary differential equations

DOI10.1016/j.jcp.2014.08.013zbMath1349.65228arXiv1401.2125OpenAlexW2139434111MaRDI QIDQ349622

Adrian Sandu, Paul Tranquilli

Publication date: 5 December 2016

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.2125

zbMATH Keywords

\textit{B}-seriesButcher treesexponential integratorKrylovtime integrator

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical computation of matrix exponential and similar matrix functions (65F60)

Related Items (11)

Linearly Implicit Multistep Methods for Time Integration ⋮ High-order numerical solutions to the shallow-water equations on the rotated cubed-sphere grid ⋮ Analytical Jacobian-vector products for the matrix-free time integration of partial differential equations ⋮ Fourth-order two-stage explicit exponential integrators for time-dependent PDEs ⋮ Jacobian-free high order local linearization methods for large systems of initial value problems ⋮ Subspace adaptivity in Rosenbrock-Krylov methods for the time integration of initial value problems ⋮ Partitioned exponential methods for coupled multiphysics systems ⋮ Linearly implicit GARK schemes ⋮ EPIRK-\(W\) and EPIRK-\(K\) time discretization methods ⋮ Biorthogonal Rosenbrock-Krylov time discretization methods ⋮ Efficient implementation of partitioned stiff exponential Runge-Kutta methods

Uses Software

• Expokit
• RODAS
• ROWMAP
• MATLAB expm

Cites Work

• Unnamed Item
• A new class of split exponential propagation iterative methods of Runge-Kutta type (sEPIRK) for semilinear systems of odes
• A new class of exponential propagation iterative methods of Runge-Kutta type (EPIRK)
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• Numerical experiments with Krylov integrators
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• Matrix-free \(W\)-methods using a multiple Arnoldi iteration
• Comparative performance of exponential, implicit, and explicit integrators for stiff systems of ODEs
• Algebraic structures of B-series
• Explicit exponential Runge-Kutta methods of high order for parabolic problems
• Some secant approximations for Rosenbrock \(W\)-methods
• Efficient integration of large stiff systems of ODEs with exponential propagation iterative (EPI) methods
• New Rosenbrock W-methods of order 3 for partial differential algebraic equations of index
• Rosenbrock--Krylov Methods for Large Systems of Differential Equations
• Expokit
• Composite Schemes for Conservation Laws
• Exponential Integrators for Large Systems of Differential Equations
• Iterative Krylov Methods for Large Linear Systems
• Trees, B-series and exponential integrators
• Exponential Rosenbrock-Type Methods
• The Scaling and Squaring Method for the Matrix Exponential Revisited

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