Total-variation-diminishing time discretizations
SIAM Journal on Scientific and Statistical Computing
A positive finite-difference advection scheme
Journal of Computational Physics
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
Implicit-explicit Runge-Kutta schemes for stiff systems of differential equations
Recent trends in numerical analysis
Implicit-explicit time stepping with spatial discontinuous finite elements
Applied Numerical Mathematics
IMEX extensions of linear multistep methods with general monotonicity and boundedness properties
Journal of Computational Physics
Linearly implicit methods for nonlinear PDEs with linear dispersion and dissipation
Journal of Computational Physics
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In this note we propose and analyze novel implicit-explicit methods based on second order strong stability preserving multistep time discretizations. Several schemes are developed, and a linear stability analysis is performed to study their properties with respect to the implicit and explicit eigenvalues. One of the proposed schemes is found to have very good stability properties, with implicit A-stability for the entire explicit stability domain. The properties of the other proposed schemes are comparable to those of traditional methods found in the literature.