Variable step implementation of ETD methods for semilinear problems

DOI10.1016/j.amc.2007.06.025zbMath1135.65370OpenAlexW2060274591MaRDI QIDQ2479127

M. P. Calvo, A. M. Portillo

Publication date: 26 March 2008

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

Full work available at URL: https://doi.org/10.1016/j.amc.2007.06.025

zbMATH Keywords

numerical resultsstiff systemsevolution equationserror estimatesemidiscretizationsemilinear equationsimplementationexponential integratorsmultistep methodexponential time differencing methodsvariable steps

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Nonlinear ordinary differential equations and systems (34A34) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (4)

Fast high-order compact exponential time differencing Runge-Kutta methods for second-order semilinear parabolic equations ⋮ Exponential almost Runge-Kutta methods for semilinear problems ⋮ A 17th-order radau IIA method for package \texttt{RADAU}. Applications in mechanical systems ⋮ An accurate approximation of exponential integrators for the Schrödinger equation

Uses Software

• RODAS
• Expint

Cites Work

• Exponential time differencing for stiff systems
• Generalized integrating factor methods for stiff PDEs
• Stability of multistep-methods on variable grids
• A class of explicit multistep exponential integrators for semilinear problems
• Implementation of exponential Rosenbrock-type integrators
• Semigroups of linear operators and applications to partial differential equations
• Geometric theory of semilinear parabolic equations
• A new class of time discretization schemes for the solution of nonlinear PDEs
• Exponential Runge-Kutta methods for parabolic problems.
• Exponential integrators for quantum-classical molecular dynamics
• A class of explicit exponential general linear methods
• Exponential Integrators for Large Systems of Differential Equations
• Fourth-Order Time-Stepping for Stiff PDEs
• Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems

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