770 research outputs found
A Parameterized multi-step Newton method for solving systems of nonlinear equations
We construct a novel multi-step iterative method for solving systems of nonlinear equations by introducing a parameter. to generalize the multi-step Newton method while keeping its order of convergence and computational cost. By an appropriate selection of theta, the new method can both have faster convergence and have larger radius of convergence. The new iterative method only requires one Jacobian inversion per iteration, and therefore, can be efficiently implemented using Krylov subspace methods. The new method can be used to solve nonlinear systems of partial differential equations, such as complex generalized Zakharov systems of partial differential equations, by transforming them into systems of nonlinear equations by discretizing approaches in both spatial and temporal independent variables such as, for instance, the Chebyshev pseudo-spectral discretizing method. Quite extensive tests show that the new method can have significantly faster convergence and significantly larger radius of convergence than the multi-step Newton method.Peer ReviewedPostprint (author's final draft
Numerical simulation of surface waves instability on a discrete grid
We perform full-scale numerical simulation of instability of weakly nonlinear
waves on the surface of deep fluid. We show that the instability development
leads to chaotization and formation of wave turbulence.
We study instability both of propagating and standing waves. We studied
separately pure capillary wave unstable due to three-wave interactions and pure
gravity waves unstable due to four-wave interactions. The theoretical
description of instabilities in all cases is included into the article. The
numerical algorithm used in these and many other previous simulations performed
by authors is described in details.Comment: 47 pages, 40 figure
Determination of the strange quark mass from Cabibbo-suppressed tau decays with resummed perturbation theory in an effective scheme
We present an analysis of the m_s^2-corrections to Cabibbo-suppressed tau
lepton decays employing contour improved resummation within an effective scheme
which is an essential new feature as compared to previous analyses. The whole
perturbative QCD dynamics of the tau-system is described by the beta-function
of the effective coupling constant and by two gamma-functions for the effective
mass parameters of the strange quark in different spin channels. We analyze the
stability of our results with regard to high-order terms in the perturbative
expansion of the renormalization group functions. A numerical value for the
strange quark mass in the MS scheme is extracted m_s(M_\tau)=130\pm 27_{exp}\pm
9_{th} MeV. After running to the scale 1 GeV this translates into m_s(1
GeV)=176 \pm 37_{exp}\pm 13_{th} MeV.Comment: 32 pages, latex, 4 postscript figures, revised version to appear in
European Physical Journal C, discussion of the choice of the moments added,
some errors correcte
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