Total-variation-diminishing time discretizations
SIAM Journal on Scientific and Statistical Computing
Implicit-explicit methods for time-dependent partial differential equations
SIAM Journal on Numerical Analysis
On the stability of implicit-explicit linear multistep methods
Applied Numerical Mathematics - Special issue on time integration
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
Numerical Initial Value Problems in Ordinary Differential Equations
Numerical Initial Value Problems in Ordinary Differential Equations
Partially Implicit BDF2 Blends for Convection Dominated Flows
SIAM Journal on Numerical Analysis
Adaptive Discontinuous Galerkin Finite Element Methods for Nonlinear Hyperbolic Conservation Laws
SIAM Journal on Scientific Computing
Journal of Computational Physics
Partitioning methods for reaction-diffusion problems
Applied Numerical Mathematics
Self-adaptive time integration of flux-conservative equations with sources
Journal of Computational Physics
Implicit--explicit methods based on strong stability preserving multistep time discretizations
Applied Numerical Mathematics
Mathematics and Computers in Simulation
On an accurate third order implicit-explicit Runge--Kutta method for stiff problems
Applied Numerical Mathematics
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In this paper a combination of discontinuous, piecewise linear, finite elements with BDF2 implicit-explicit time stepping is considered for convection-reaction equations. Combined with low order quadrature rules, this leads to convenient schemes. We shall consider the effect of such low order quadrature rules on accuracy and stability for one-dimensional problems. Furthermore, attention will be given to the stability and TVD properties of the explicit BDF2-type formula used for convection in the implicit-explicit time stepping.