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41.
P.A. Ramachandran 《Numerical Methods for Partial Differential Equations》2006,22(4):831-846
Time‐dependent differential equations can be solved using the concept of method of lines (MOL) together with the boundary element (BE) representation for the spatial linear part of the equation. The BE method alleviates the need for spatial discretization and casts the problem in an integral format. Hence errors associated with the numerical approximation of the spatial derivatives are totally eliminated. An element level local cubic approximation is used for the variable at each time step to facilitate the time marching and the nonlinear terms are represented in a semi‐implicit manner by a local linearization at each time step. The accuracy of the method has been illustrated on a number of test problems of engineering significance. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006 相似文献
42.
We present a new approach to study the convergence of Newton's method in Banach spaces, which relax the conditions appearing in the usual studies. The approach is based on the bound required for the second derivative of the operator involved. An application to a nonlinear integral equation is presented. 相似文献
43.
A. B. Mazo 《Fluid Dynamics》2002,37(6):913-918
Plane ideal incompressible flow in a rectangular channel partitioned by a thin permeable barrier (lattice) is considered. In flowing through the lattice the stream suddenly (jumpwise) changes direction and loses energy. The flow is assumed to be vortical; the vorticity is discontinuous on the lattice. A mathematical formulation of the problem for the stream function is proposed in the form of a nonlinear elliptic equation with coefficients discontinuous on the lattice line. A numerical solution is constructed using the finite-element iteration method. The results of the numerical simulation show how the flow velocity profile in the channel can be controlled by means of permeable barriers. 相似文献
44.
A simple scheme is developed for treatment of vertical bed topography in shallow water flows. The effect of the vertical step on flows is modelled with the shallow water equations including local energy loss terms. The bed elevation is denoted with zb‐ for the left and zb+ for the right values at each grid point, hence exactly representing a discontinuity in the bed topography. The surface gradient method (SGM) is generalized to reconstruct water depths at cell interfaces involving a vertical step so that the fluxes at the cell interfaces can accurately be calculated with a Riemann solver. The scheme is verified by predicting a surge crossing a step, a tidal flow over a step and dam‐break flows on wet/dry beds. The results have shown good agreements compared with analytical solutions and available experimental data. The scheme is efficient, robust, and may be used for practical flow calculations. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
45.
We obtain a solution of the DGLAP equation for the gluon at low x first by expanding the gluon in a Taylor series and then using the method of characteristics. We test its validity by comparing
it with that of Glück, Reya and Vogt. The convergence criteria of the approximation used are also discussed. We also calculate
εF
2(x,Q)2/ε In Q
2 using its approximate relations with the gluon distribution at low x. The predictions are then compared with the HERA data. 相似文献
46.
M. Gorkunov M. Lapine E. Shamonina K.H. Ringhofer 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,28(3):263-269
Effective magnetic properties of a composite meta-material consisting of periodically arranged circular conductive elements
are studied theoretically. A general expression for the effective bulk permeability is obtained with mutual effects and lattice
ordering being taken into account. The resonance frequency of the permeability is found to be strongly dependent on the size
and shape of the unit cell. Frequency dispersion of the permeability is studied with special attention paid to the frequency
range, where negative values of the permeability are possible. Corresponding recommendations for optimisation of the meta-materials
with negative permeability are made. The results are confirmed by numerical simulations of the finite structure behaviour
in an external magnetic field.
Received 19 April 2002 Published online 31 July 2002 相似文献
47.
48.
The investigative results of modulated pulse output from an LD end-pumped passively Q-switched intracavity-frequency-doubling Nd∶YVO4/KTP laser with Cr4+∶YAG saturable absorber are presented. The numerical stimulations of these modulated pulses are carried out basing on the rate equations. It indicated that the modulations are attribute to the frequency beating of two eigenstates of the resonant polarized modes. The theoretical calculations are in good agreement with the experimental observations. 相似文献
49.
采用基于第一原理的全势能线性缀加平面波加局域轨道((L)APW lo)方法对Nd(Fe,Si)11Cx化合物(x=0,2)的电子结构进行了计算,得到了化合物态密度和磁矩等信息.计算结果表明NdFe9Si2化合物中Si原子主要与4b和32i位Fe原子产生杂化,导致Fe原子磁矩减小.NdFe9Si2C2化合物C原子使32i位Fe原子磁矩进一步降低,同时减弱了Si原子的影响,使得4b位Fe原子磁矩增大. 相似文献
50.
A. G. Bratsos 《Numerical Algorithms》2006,43(4):295-308
A three-time level finite-difference scheme based on a fourth order in time and second order in space approximation has been
proposed for the numerical solution of the nonlinear two-dimensional sine-Gordon equation. The method, which is analysed for
local truncation error and stability, leads to the solution of a nonlinear system. To avoid solving it, a predictor–corrector
scheme using as predictor a second-order explicit scheme is proposed. The procedure of the corrector has been modified by
considering as known the already evaluated corrected values instead of the predictor ones. This modified scheme has been tested
on the line and circular ring soliton and the numerical experiments have proved that there is an improvement in the accuracy
over the standard predictor–corrector implementation.
This research was co-funded by E.U. (75%) and by the Greek Government (25%). 相似文献