A New Class of High-Order Methods for Multirate Differential Equations

DOI10.1137/19M125621XzbMath1441.65061arXiv1904.06474MaRDI QIDQ5112549

Rujeko Chinomona, Vu Thai Luan, Daniel R. Reynolds

Publication date: 29 May 2020

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.06474

zbMATH Keywords

exponential integratorsexponential Runge-Kutta methodsmultirate time integrationmultiple time stepping

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) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (5)

Multirate Exponential Rosenbrock Methods ⋮ Adaptive Time Step Control for Multirate Infinitesimal Methods ⋮ Implicit-explicit multirate infinitesimal stage-restart methods ⋮ Implicit-Explicit Multirate Infinitesimal GARK Methods ⋮ MERK

Uses Software

• Algorithm 919
• phipm
• GitHub

Cites Work

• Unnamed Item
• A linearly fourth order multirate Runge-Kutta method with error control
• Fourth-order two-stage explicit exponential integrators for time-dependent PDEs
• Numerical solution of multiscale problems in atmospheric modeling
• Exponential multistep methods of Adams-type
• A posteriori analysis of a multirate numerical method for ordinary differential equations
• Exponential time differencing for stiff systems
• Multirate generalized additive Runge Kutta methods
• Efficient multiple time-stepping algorithms of higher order
• A multirate time stepping strategy for stiff ordinary differential equations
• A multirate time integrator for regularized Stokeslets
• Explicit local time-stepping methods for Maxwell's equations
• Multirate Runge-Kutta schemes for advection equations
• Implicit-explicit Runge-Kutta methods for computing atmospheric reactive flows
• Exponential Runge-Kutta methods for parabolic problems.
• High-order explicit local time-stepping methods for damped wave equations
• Extrapolated multirate methods for differential equations with multiple time scales
• Parallel exponential Rosenbrock methods
• Exponential Rosenbrock methods of order five -- construction, analysis and numerical comparisons
• Further development of efficient and accurate time integration schemes for meteorological models
• Explicit exponential Runge-Kutta methods of high order for parabolic problems
• Multirate infinitesimal step methods for atmospheric flow simulation
• Exponential integrators
• A Generalized-Structure Approach to Additive Runge--Kutta Methods
• Algorithm 919
• Extrapolated Implicit-Explicit Time Stepping
• Solving Ordinary Differential Equations I
• A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides
• On Krylov Subspace Approximations to the Matrix Exponential Operator
• Exponential Integrators for Large Systems of Differential Equations
• Design of High-Order Decoupled Multirate GARK Schemes
• Coupled Multirate Infinitesimal GARK Schemes for Stiff Systems with Multiple Time Scales
• A Class of Multirate Infinitesimal GARK Methods
• Exponential B-Series: The Stiff Case
• Explicit local time-stepping methods for time-dependent wave propagation
• Geometric Numerical Integration
• Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems
• Multirate partitioned Runge-Kutta methods

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