Exponential multistep methods of Adams-type

DOI10.1007/s10543-011-0332-6zbMath1237.65071OpenAlexW2088291843MaRDI QIDQ657891

Marlis Hochbruck, Alexander Ostermann

Publication date: 10 January 2012

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://publikationen.bibliothek.kit.edu/1000041812

zbMATH Keywords

convergencenumerical experimentsevolution equationslocal time steppinganalysis of error behaviourexponential Adams methodsexponential integrators for stiff IVPsfixed step-sizelinearized exponential multistep methods

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for numerical methods for ordinary differential equations (65L70) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items

Equivalence between the DPG method and the exponential integrators for linear parabolic problems, Computational study of multi-species fractional reaction-diffusion system with ABC operator, Locally linearized Runge-Kutta method of Dormand and Prince for large systems of initial value problems, High-order numerical solutions to the shallow-water equations on the rotated cubed-sphere grid, Stability analysis of explicit exponential integrators for delay differential equations, A family of Adams exponential integrators for fractional linear systems, On the time-fractional Schrödinger equation: theoretical analysis and numerical solution by matrix Mittag-Leffler functions, Spatiotemporal patterns in the Belousov-Zhabotinskii reaction systems with Atangana-Baleanu fractional order derivative, Solution of pattern waves for diffusive Fisher-like non-linear equations with adaptive methods, Full discretization error analysis of exponential integrators for semilinear wave equations, A high-order exponential integrator for nonlinear parabolic equations with nonsmooth initial data, Error representation of the time-marching DPG scheme, Combining DPG in space with DPG time-marching scheme for the transient advection-reaction equation, A stabilized second order exponential time differencing multistep method for thin film growth model without slope selection, A second-order exponential time differencing multi-step energy stable scheme for Swift-Hohenberg equation with quadratic-cubic nonlinear term, A New Class of High-Order Methods for Multirate Differential Equations, Rush-Larsen time-stepping methods of high order for stiff problems in cardiac electrophysiology, Upwind discontinuous Galerkin space discretization and locally implicit time integration for linear Maxwell’s equations, Unnamed Item, High order explicit exponential Runge-Kutta methods for semilinear delay differential equations, Exponential integrators for large-scale stiff Riccati differential equations, Multi-level explicit local time-stepping methods for second-order wave equations, Convergence Analysis of Energy Conserving Explicit Local Time-Stepping Methods for the Wave Equation, Analysis of Mathematics and Numerical Pattern Formation in Superdiffusive Fractional Multicomponent System, Fast numerical schemes for nonlinear space-fractional multidelay reaction-diffusion equations by implicit integration factor methods, Exponential Time Differencing Gauge Method for Incompressible Viscous Flows, Mathematical study of multispecies dynamics modeling predator-prey spatial interactions, Exponential Adams-Bashforth integrators for stiff ODEs, application to cardiac electrophysiology, Solving periodic semilinear stiff PDEs in 1D, 2D and 3D with exponential integrators, Explicit exponential Runge-Kutta methods for semilinear parabolic delay differential equations, D-convergence and conditional GDN-stability of exponential Runge-Kutta methods for semilinear delay differential equations, A DPG-based time-marching scheme for linear hyperbolic problems, On averaged exponential integrators for semilinear wave equations with solutions of low-regularity, Numerical simulations of chaotic and complex spatiotemporal patterns in fractional reaction-diffusion systems, Efficient multiple time-stepping algorithms of higher order, Efficient computation of phi-functions in exponential integrators, Further development of efficient and accurate time integration schemes for meteorological models, Convergence of rational multistep methods of Adams-Padé type, Energy stable higher-order linear ETD multi-step methods for gradient flows: application to thin film epitaxy, A third order exponential time differencing numerical scheme for no-slope-selection epitaxial thin film model with energy stability, Runge--Kutta-Based Explicit Local Time-Stepping Methods for Wave Propagation, Computing high dimensional multiple integrals involving matrix exponentials

Cites Work

• Exponential time differencing for stiff systems
• A class of explicit multistep exponential integrators for semilinear problems
• Explicit local time-stepping methods for Maxwell's equations
• Semigroups of linear operators and applications to partial differential equations
• Geometric theory of semilinear parabolic equations
• On generalized linear multistep methods with zero-parasitic roots and an adaptive principal root
• Efficient integration of large stiff systems of ODEs with exponential propagation iterative (EPI) methods
• A class of explicit exponential general linear methods
• Exponential integrators
• Solving Ordinary Differential Equations I
• One-Parameter Semigroups for Linear Evolution Equations
• Exponential Integrators for Large Systems of Differential Equations
• Exponential Rosenbrock-Type Methods
• Multistep Methods with Variable Matrix Coefficients
• An exponential method of numerical integration of ordinary differential equations