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math.NA2017★ 12 cited
Runge-Kutta-Gegenbauer explicit methods for advection-diffusion problems
Stephen O'Sullivan
In this paper, Runge-Kutta-Gegenbauer (RKG) stability polynomials of arbitrarily high order of accuracy are introduced in closed form. The stability domain of RKG polynomials exten…
math.NA2017★ 4 cited
Factorized Runge-Kutta-Chebyshev Methods
Stephen O'Sullivan
The second-order extended stability Factorized Runge-Kutta-Chebyshev (FRKC2) class of explicit schemes for the integration of large systems of PDEs with diffusive terms is presente…