IMEX extensions of linear multistep methods with general monotonicity and boundedness properties

Authors:
Willem Hundsdorfer;Steven J. Ruuth
Affiliations:
CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands;Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
Venue:
Journal of Computational Physics
Year:
2007

Citing 12
Cited 10

Total-variation-diminishing time discretizations

SIAM Journal on Scientific and Statistical Computing
Runge-Kutta approximation of quasi-linear parabolic equations

Mathematics of Computation
Interior estimates for time discretizations of parabolic equations

NUMDIFF-7 Selected papers of the seventh conference on Numerical treatment of differential equations
Implicit-explicit methods for time-dependent partial differential equations

SIAM Journal on Numerical Analysis
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations

Applied Numerical Mathematics - Special issue on time integration
On the stability of implicit-explicit linear multistep methods

Applied Numerical Mathematics - Special issue on time integration
Linearly implicit Runge—Kutta methods for advection—reaction—diffusion equations

Applied Numerical Mathematics
Additive Runge-Kutta schemes for convection-diffusion-reaction equations

Applied Numerical Mathematics
Semi-implicit projection methods for incompressible flow based on spectral deferred corrections

Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
High-order linear multistep methods with general monotonicity and boundedness properties

Journal of Computational Physics
Implicit---Explicit Runge---Kutta Schemes and Applications to Hyperbolic Systems with Relaxation

Journal of Scientific Computing
Implicit--explicit methods based on strong stability preserving multistep time discretizations

Applied Numerical Mathematics

High Order Strong Stability Preserving Time Discretizations

Journal of Scientific Computing
Extrapolated Implicit-Explicit Time Stepping

SIAM Journal on Scientific Computing
Semi-Lagrangian multistep exponential integrators for index 2 differential-algebraic systems

Journal of Computational Physics
Linearly implicit methods for nonlinear PDEs with linear dispersion and dissipation

Journal of Computational Physics
Stability of two IMEX methods, CNLF and BDF2-AB2, for uncoupling systems of evolution equations

Applied Numerical Mathematics
Stepsize Restrictions for Boundedness and Monotonicity of Multistep Methods

Journal of Scientific Computing
A collocated method for the incompressible Navier-Stokes equations inspired by the Box scheme

Journal of Computational Physics
Summation-by-parts in time

Journal of Computational Physics
Multiphysics simulations: Challenges and opportunities

International Journal of High Performance Computing Applications
Extrapolation-based implicit-explicit general linear methods

Numerical Algorithms

Quantified Score

Hi-index	31.50

Visualization

Abstract

For solving hyperbolic systems with stiff sources or relaxation terms, time stepping methods should combine favorable monotonicity properties for shocks and steep solution gradients with good stability properties for stiff terms. In this paper we consider implicit-explicit (IMEX) multistep methods. Suitable methods will be constructed, based on explicit methods with general monotonicity and boundedness properties for hyperbolic equations. Numerical comparisons are made with several implicit-explicit Runge-Kutta methods.