Unconditional stability of explicit exponential Runge-Kutta methods for semi-linear ordinary differential equations

DOI10.1090/S0025-5718-08-02171-6zbMath1198.65127MaRDI QIDQ3055126

Stefano Maset, Marino Zennaro

Publication date: 7 November 2010

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

stability analysisordinary differential equationsinitial value problemsexponential Runge-Kutta methods

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)

Related Items (20)

Convergence and stability of exponential integrators for semi-linear stochastic pantograph integro-differential equations with jump ⋮ Up to fourth-order unconditionally structure-preserving parametric single-step methods for semilinear parabolic equations ⋮ THE NUMERICAL STABILITY OF STOCHASTIC ORDINARY DIFFERENTIAL EQUATIONS WITH ADDITIVE NOISE ⋮ Stability analysis of explicit exponential integrators for delay differential equations ⋮ Exponential Runge-Kutta methods for delay differential equations ⋮ Exponential Runge-Kutta for the inhomogeneous Boltzmann equations with high order of accuracy ⋮ Convergence and Mean-Square Stability of Exponential Euler Method for Semi-Linear Stochastic Delay Integro-Differential Equations ⋮ Exponential almost Runge-Kutta methods for semilinear problems ⋮ A family of structure-preserving exponential time differencing Runge-Kutta schemes for the viscous Cahn-Hilliard equation ⋮ Exponential Additive Runge-Kutta Methods for Semi-Linear Differential Equations ⋮ High order explicit exponential Runge-Kutta methods for semilinear delay differential equations ⋮ Explicit exponential Runge-Kutta methods for semilinear parabolic delay differential equations ⋮ Stability analysis of exponential Runge-Kutta methods for delay differential equations ⋮ The convergence and MS stability of exponential Euler method for semilinear stochastic differential equations ⋮ Structure-preserving Exponential Runge--Kutta Methods ⋮ D-convergence and conditional GDN-stability of exponential Runge-Kutta methods for semilinear delay differential equations ⋮ Numerical methods for kinetic equations ⋮ Asymptotical stability of numerical methods for semi-linear impulsive differential equations ⋮ Matrix transfer technique for anomalous diffusion equation involving fractional Laplacian ⋮ A uniformly accurate numerical method for a class of dissipative systems

Uses Software

• Expint

Cites Work

• Unnamed Item
• Exponential time differencing for stiff systems
• Generalized integrating factor methods for stiff PDEs
• B-convergence results for linearly implicit one step methods
• Contractivity of Runge-Kutta methods
• A new class of time discretization schemes for the solution of nonlinear PDEs
• High order Runge-Kutta methods on manifolds
• An evaluation of explicit pseudo-steady-state approximation schemes for stiff ODE systems from chemical kinetics
• Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
• Exponential Runge-Kutta methods for parabolic problems.
• A Gautschi-type method for oscillatory second-order differential equations
• Exponential integrators for quantum-classical molecular dynamics
• An operator-integration-factor splitting method for time-dependent problems: Application to incompressible fluid flow
• On Logarithmic Norms
• On Krylov Subspace Approximations to the Matrix Exponential Operator
• Exponential Integrators for Large Systems of Differential Equations
• Implicit-Explicit Methods for Time-Dependent Partial Differential Equations
• Fourth-Order Time-Stepping for Stiff PDEs
• Generalized Runge-Kutta Processes for Stable Systems with Large Lipschitz Constants
• Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems
• A quasi-steady-state solver for the stiff ordinary differential equations of reaction kinetics

This page was built for publication: Unconditional stability of explicit exponential Runge-Kutta methods for semi-linear ordinary differential equations