RKC time-stepping for advection-diffusion-reaction problems
Journal of Computational Physics
Efficient semi-implicit schemes for stiff systems
Journal of Computational Physics
Self-adaptive time integration of flux-conservative equations with sources
Journal of Computational Physics
IRKC: an IMEX solver for stiff diffusion-reaction PDEs
Journal of Computational and Applied Mathematics
Runge-Kutta-Chebyshev projection method
Journal of Computational Physics
On stabilized integration for time-dependent PDEs
Journal of Computational Physics
IMEX Runge-Kutta schemes for reaction-diffusion equations
Journal of Computational and Applied Mathematics
A stabilized explicit Lagrange multiplier based domain decomposition method for parabolic problems
Journal of Computational Physics
An Eulerian--Lagrangian method for coupled parabolic-hyperbolic equations
Applied Numerical Mathematics
An iterated Radau method for time-dependent PDEs
Journal of Computational and Applied Mathematics
SIAM Journal on Numerical Analysis
Extrapolated Implicit-Explicit Time Stepping
SIAM Journal on Scientific Computing
Partitioned Runge-Kutta-Chebyshev Methods for Diffusion-Advection-Reaction Problems
SIAM Journal on Scientific Computing
Parallelization of implicit-explicit runge-kutta methods for cluster of PCs
Euro-Par'05 Proceedings of the 11th international Euro-Par conference on Parallel Processing
Numerical approximation of Turing patterns in electrodeposition by ADI methods
Journal of Computational and Applied Mathematics
A variable time-step-size code for advection-diffusion-reaction PDEs
Applied Numerical Mathematics
Multiphysics simulations: Challenges and opportunities
International Journal of High Performance Computing Applications
Stabilized explicit Runge-Kutta methods for multi-asset American options
Computers & Mathematics with Applications
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An implicit-explicit (IMEX) extension of the explicit Runge--Kutta--Chebyshev (RKC) scheme designed for parabolic PDEs is proposed for diffusion-reaction problems with severely stiff reaction terms. The IMEX scheme treats these reaction terms implicitly and diffusion terms explicitly. Within the setting of linear stability theory, the new IMEX scheme is unconditionally stable for reaction terms having a Jacobian matrix with a real spectrum. For diffusion terms the stability characteristics remain unchanged. A numerical comparison for a stiff, nonlinear radiation-diffusion problem between an RKC solver, an IMEX-RKC solver, and the popular implicit BDF solver VODPK using the Krylov solver GMRES illustrates the excellent performance of the new scheme.