2,357 research outputs found
Runge-Kutta-Gegenbauer explicit methods for advection-diffusion problems
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 extends in the the real direction with the square of
polynomial degree, and in the imaginary direction as an increasing function of
Gegenbauer parameter. Consequently, the polynomials are naturally suited to the
construction of high order stabilized Runge-Kutta (SRK) explicit methods for
systems of PDEs of mixed hyperbolic-parabolic type.
We present SRK methods composed of ordered forward Euler stages, with
complex-valued stepsizes derived from the roots of RKG stability polynomials of
degree . Internal stability is maintained at large stage number through an
ordering algorithm which limits internal amplification factors to .
Test results for mildly stiff nonlinear advection-diffusion-reaction problems
with moderate () mesh P\'eclet numbers are provided at second,
fourth, and sixth orders, with nonlinear reaction terms treated by complex
splitting techniques above second order.Comment: 20 pages, 7 figures, 3 table
Hamevol1.0: a C++ code for differential equations based on Runge-Kutta algorithm. An application to matter enhanced neutrino oscillation
We present a C++ implementation of a fifth order semi-implicit Runge-Kutta
algorithm for solving Ordinary Differential Equations. This algorithm can be
used for studying many different problems and in particular it can be applied
for computing the evolution of any system whose Hamiltonian is known. We
consider in particular the problem of calculating the neutrino oscillation
probabilities in presence of matter interactions. The time performance and the
accuracy of this implementation is competitive with respect to the other
analytical and numerical techniques used in literature. The algorithm design
and the salient features of the code are presented and discussed and some
explicit examples of code application are given.Comment: 18 pages, Late
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