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Full-Text Articles in Physical Sciences and Mathematics
A Class Of High-Order Runge-Kutta-Chebyshev Stability Polynomials, Stephen O'Sullivan
A Class Of High-Order Runge-Kutta-Chebyshev Stability Polynomials, Stephen O'Sullivan
Articles
The analytic form of a new class of factorized Runge-Kutta-Chebyshev (FRKC) stability polynomials of arbitrary order N is presented. Roots of FRKC stability polynomials of degree L = MN are used to construct explicit schemes comprising L forward Euler stages with internal stability ensured through a sequencing algorithm which limits the internal amplification factors to ~ L2. The associated stability domain scales as M2 along the real axis. Marginally stable real-valued points on the interior of the stability domain are removed via a prescribed damping procedure. By construction, FRKC schemes meet all linear order conditions; for nonlinear …
On The Dynamics Of Internal Waves Interacting With The Equatorial Undercurrent, Alan Compelli, Rossen Ivanov
On The Dynamics Of Internal Waves Interacting With The Equatorial Undercurrent, Alan Compelli, Rossen Ivanov
Articles
The interaction of the nonlinear internal waves with a nonuniform current with a specific form, characteristic for the equatorial undercurrent, is studied. The current has no vorticity in the layer, where the internal wave motion takes place. We show that the nonzero vorticity that might be occuring in other layers of the current does not affect the wave motion. The equations of motion are formulated as a Hamiltonian system.