Solving parabolic integro-differential equations by an explicit integration method
Journal of Computational and Applied Mathematics
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
RKC: an explicit solver for parabolic PDEs
Journal of Computational and Applied Mathematics
Linearly implicit Runge—Kutta methods for advection—reaction—diffusion equations
Applied Numerical Mathematics
Fourth Order Chebyshev Methods with Recurrence Relation
SIAM Journal on Scientific Computing
Additive Runge-Kutta schemes for convection-diffusion-reaction equations
Applied Numerical Mathematics
An Implicit-Explicit Runge--Kutta--Chebyshev Scheme for Diffusion-Reaction Equations
SIAM Journal on Scientific Computing
RKC time-stepping for advection-diffusion-reaction problems
Journal of Computational Physics
IRKC: an IMEX solver for stiff diffusion-reaction PDEs
Journal of Computational and Applied Mathematics
Principles of Computational Fluid Dynamics
Principles of Computational Fluid Dynamics
On stabilized integration for time-dependent PDEs
Journal of Computational Physics
S-ROCK: Chebyshev Methods for Stiff Stochastic Differential Equations
SIAM Journal on Scientific Computing
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An integration method based on Runge-Kutta-Chebyshev (RKC) methods is discussed which has been designed to treat moderately stiff and nonstiff terms separately. The method, called partitioned Runge-Kutta-Chebyshev (PRKC), is a one-step, partitioned RK method of second order. It belongs to the class of stabilized methods, namely explicit RK methods possessing extended real stability intervals. The aim of the PRKC method is to reduce the number of function evaluations of the nonstiff terms and to get a nonzero imaginary stability boundary.