Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Applied Numerical Mathematics - Special issue: a festschrift to honor Professor Robert Vichnevetsky on his 65th birthday
RKC: an explicit solver for parabolic PDEs
Journal of Computational and Applied Mathematics
Fourth Order Chebyshev Methods with Recurrence Relation
SIAM Journal on Scientific Computing
A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods
SIAM Journal on Numerical Analysis
An Implicit-Explicit Runge--Kutta--Chebyshev Scheme for Diffusion-Reaction Equations
SIAM Journal on Scientific Computing
Principles of Computational Fluid Dynamics
Principles of Computational Fluid Dynamics
Runge-Kutta-Chebyshev projection method
Journal of Computational Physics
Numerical methods for modelling leaching of pollutants in soils
Advances in Engineering Software
On stabilized integration for time-dependent PDEs
Journal of Computational Physics
A stabilized explicit Lagrange multiplier based domain decomposition method for parabolic problems
Journal of Computational Physics
Performance of stabilized explicit time integration methods for parallel air quality models
SpringSim '07 Proceedings of the 2007 spring simulation multiconference - Volume 2
An Eulerian--Lagrangian method for coupled parabolic-hyperbolic equations
Applied Numerical Mathematics
Journal of Scientific Computing
A high-order low-Mach number AMR construction for chemically reacting flows
Journal of Computational Physics
Journal of Computational Physics
Partitioned Runge-Kutta-Chebyshev Methods for Diffusion-Advection-Reaction Problems
SIAM Journal on Scientific Computing
An Efficient NRxx Method for Boltzmann-BGK Equation
Journal of Scientific Computing
Modelling and simulation of a polluted water pumping process
Mathematical and Computer Modelling: An International Journal
A variable time-step-size code for advection-diffusion-reaction PDEs
Applied Numerical Mathematics
A ghost fluid method for compressible reacting flows with phase change
Journal of Computational Physics
Accelerating moderately stiff chemical kinetics in reactive-flow simulations using GPUs
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Stabilized explicit Runge-Kutta methods for multi-asset American options
Computers & Mathematics with Applications
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The original explicit Runge-Kutta-Chebyshev (RKC) method is a stabilized second-order integration method for pure diffusion problems. Recently, it has been extended in an implicit explicit manner to also incorporate highly stiff reaction terms. This implicit-explicit RKC method thus treats diffusion terms explicitly and the highly stiff reaction terms implicitly. The current paper deals with the incorporation of advection terms for the explicit method, thus aiming at the implicit-explicit RKC integration of advection-diffusion-reaction equations in a manner that advection and diffusion terms are treated simultaneously and explicitly and the highly stiff reaction terms implicitly.