Total-variation-diminishing time discretizations
SIAM Journal on Scientific and Statistical Computing
A model for nonlinear seismic waves in a medium with instability
Proceedings of the twelfth annual international conference of the Center for Nonlinear Studies on Nonlinearity in Materials Science
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
Symplectic Methods Based on Decompositions
SIAM Journal on Numerical Analysis
Exponential Integrators for Large Systems of Differential Equations
SIAM Journal on Scientific Computing
A new class of time discretization schemes for the solution of nonlinear PDEs
Journal of Computational Physics
A fast spectral algorithm for nonlinear wave equations with linear dispersion
Journal of Computational Physics
Linearly implicit Runge—Kutta methods for advection—reaction—diffusion equations
Applied Numerical Mathematics
Exponential time differencing for stiff systems
Journal of Computational Physics
Partially Implicit BDF2 Blends for Convection Dominated Flows
SIAM Journal on Numerical Analysis
A composite Runge-Kutta method for the spectral solution of semilinear PDEs
Journal of Computational Physics
Additive Runge-Kutta schemes for convection-diffusion-reaction equations
Applied Numerical Mathematics
Fourth-Order Time-Stepping for Stiff PDEs
SIAM Journal on Scientific Computing
Generalized integrating factor methods for stiff PDEs
Journal of Computational Physics
Explicit Exponential Runge-Kutta Methods for Semilinear Parabolic Problems
SIAM Journal on Numerical Analysis
High-order linear multistep methods with general monotonicity and boundedness properties
Journal of Computational Physics
B-series and Order Conditions for Exponential Integrators
SIAM Journal on Numerical Analysis
Implicit---Explicit Runge---Kutta Schemes and Applications to Hyperbolic Systems with Relaxation
Journal of Scientific Computing
EXPINT---A MATLAB package for exponential integrators
ACM Transactions on Mathematical Software (TOMS)
Implicit--explicit methods based on strong stability preserving multistep time discretizations
Applied Numerical Mathematics
IMEX extensions of linear multistep methods with general monotonicity and boundedness properties
Journal of Computational Physics
Comparison of methods for evaluating functions of a matrix exponential
Applied Numerical Mathematics
On an accurate third order implicit-explicit Runge--Kutta method for stiff problems
Applied Numerical Mathematics
Semi-Lagrangian Runge-Kutta Exponential Integrators for Convection Dominated Problems
Journal of Scientific Computing
Rooted tree analysis of Runge-Kutta methods with exact treatment of linear terms
Journal of Computational and Applied Mathematics
Time-stepping methods for the simulation of the self-assembly of nano-crystals in Matlab on a GPU
Journal of Computational Physics
Hi-index | 31.45 |
The linear stability of IMEX (IMplicit-EXplicit) methods and exponential integrators for stiff systems of ODEs arising in the discrete solution of PDEs is examined for nonlinear PDEs with both linear dispersion and dissipation, and a clear method of visualization of the linear stability regions is proposed. Predictions are made based on these visualizations and are supported by a series of experiments on five PDEs including quasigeostrophic equations and stratified Boussinesq equations. The experiments, involving 24 IMEX and exponential methods of third and fourth order, confirm the predictions of the linear stability analysis, that the methods are typically limited by small eigenvalues of the linear term and by eigenvalues on or near the imaginary axis rather than by large eigenvalues near the negative real axis. The experiments also demonstrate that IMEX methods achieve comparable stability to exponential methods, and that exponential methods are significantly more accurate only when the problem is nearly linear. Novel IMEX predictor-corrector methods are also derived.