Efficient exponential Runge-Kutta methods of high order: construction and implementation

DOI10.1007/s10543-020-00834-zzbMath1471.65069arXiv2009.12714OpenAlexW3125249484WikidataQ115604949 ScholiaQ115604949MaRDI QIDQ2026363

Vu Thai Luan

Publication date: 19 May 2021

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.12714

zbMATH Keywords

exponential integratorsefficient implementationexponential Runge-Kutta methodsstiff PDEs

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) 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) Numerical methods for stiff equations (65L04)

Related Items (7)

Efficient exponential time integration for simulating nonlinear coupled oscillators ⋮ Efficient exponential methods for genetic regulatory systems ⋮ Time-accurate and highly-stable explicit peer methods for stiff differential problems ⋮ High-order implicit time integration scheme based on Padé expansions ⋮ Exponentially fitted two-derivative DIRK methods for oscillatory differential equations ⋮ BAMPHI: matrix-free and transpose-free action of linear combinations of \(\varphi\)-functions from exponential integrators ⋮ On the stability of exponential integrators for non-diffusive equations

Uses Software

• Expint
• Algorithm 919
• phipm

Cites Work

• Fourth-order two-stage explicit exponential integrators for time-dependent PDEs
• An efficient exponential time integration method for the numerical solution of the shallow water equations on the sphere
• Parallel exponential Rosenbrock methods
• Exponential time differencing for mimetic multilayer Ocean models
• 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
• Efficient exponential time integration for simulating nonlinear coupled oscillators
• The Leja Method Revisited: Backward Error Analysis for the Matrix Exponential
• Exponential integrators
• Algorithm 919
• Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators
• Exponential Time Differencing Gauge Method for Incompressible Viscous Flows
• Exponential B-Series: The Stiff Case
• B-series and Order Conditions for Exponential Integrators
• Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems

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