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排序方式: 共有145条查询结果,搜索用时 93 毫秒
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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
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Athanassios G. Bratsos 《Numerical Algorithms》2007,46(1):45-58
A predictor–corrector (P-C) scheme is applied successfully to a nonlinear method arising from the use of rational approximants
to the matrix-exponential term in a three-time level recurrence relation. The resulting nonlinear finite-difference scheme,
which is analyzed for local truncation error and stability, is solved using a P-C scheme, in which the predictor and the corrector
are explicit schemes of order 2. This scheme is accelerated by using a modification (MPC) in which the already evaluated values
are used for the corrector. The behaviour of the P-C/MPC schemes is tested numerically on the Boussinesq equation already
known from the bibliography free of boundary conditions. The numerical results are derived for both the bad and the good Boussinesq
equation and conclusions from the relevant known results are derived.
相似文献
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Our new trigonometrically fitted predictor–corrector (P–C) schemes presented here are based on the well known Adams–Bashforth–Moulton methods: the predictor is based on the fifth order Adams–Bashforth scheme and the corrector on the sixth order Adams–Moulton scheme. We tested the efficiency of our newly developed schemes against well known methods, with excellent results. The numerical experiments showed that at least one of our schemes is noticeably more efficient compared to other methods, some of which are specially designed for this type of problem. It is also worth mentioning that this is the first time that sixth algebraic order trigonometrically fitted Adams–Bashforth–Moulton P–C schemes are used to efficiently solve the radial Schrödinger equation.Active Member of the European Academy of Sciences and Arts 相似文献
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A finite volume cell‐centered Lagrangian hydrodynamics approach, formulated in Cartesian frame, is presented for solving elasto‐plastic response of solids in general unstructured grids. Because solid materials can sustain significant shear deformation, evolution equations for stress and strain fields are solved in addition to mass, momentum, and energy conservation laws. The total stress is split into deviatoric shear stress and dilatational components. The dilatational response of the material is modeled using the Mie‐Grüneisen equation of state. A predicted trial elastic deviatoric stress state is evolved assuming a pure elastic deformation in accordance with the hypo‐elastic stress‐strain relation. The evolution equations are advanced in time by constructing vertex velocity and corner traction force vectors using multi‐dimensional Riemann solutions erected at mesh vertices. Conservation of momentum and total energy along with the increase in entropy principle are invoked for computing these quantities at the vertices. Final state of deviatoric stress is effected via radial return algorithm based on the J‐2 von Mises yield condition. The scheme presented in this work is second‐order accurate both in space and time. The suitability of the scheme is evinced by solving one‐ and two‐dimensional benchmark problems both in structured grids and in unstructured grids with polygonal cells. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
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An improved class of Boussinesq systems of an arbitrary order using a wave surface elevation and velocity potential formulation is derived. Dissipative effects and wave generation due to a time‐dependent varying seabed are included. Thus, high‐order source functions are considered. For the reduction of the system order and maintenance of some dispersive characteristics of the higher‐order models, an extra O(μ2n+2) term (n ∈ ?) is included in the velocity potential expansion. We introduce a nonlocal continuous/discontinuous Galerkin FEM with inner penalty terms to calculate the numerical solutions of the improved fourth‐order models. The discretization of the spatial variables is made using continuous P2 Lagrange elements. A predictor‐corrector scheme with an initialization given by an explicit Runge–Kutta method is also used for the time‐variable integration. Moreover, a CFL‐type condition is deduced for the linear problem with a constant bathymetry. To demonstrate the applicability of the model, we considered several test cases. Improved stability is achieved. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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安装于紫金山天文台盱眙观测站用以观测近地天体的大型Schmidt望远镜,采用了平场Schmidt光学系统,改正镜通光口径为1m,球面反射镜口径为1.2m,焦距为1.8m,接收器用了4K×4K的高灵敏度CCD。本文叙述了该仪器光轴调整的方法及调整后观测获得的初步结果。叙述了望远镜光轴校正方法、校正结果、CCD靶面的调整及望远镜极轴高度、方位的调整及相应的照片。经实际观测的结果是:露光1s可拍到18等星;露光4s可拍到19.3等星;露光20s可拍摄到21.2等星。 相似文献
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合肥光源直线加速器BPM系统的研制和测量 总被引:1,自引:0,他引:1
合肥光源直线加速器新改造的BPM系统已经安装, 并做了在线的束流位置测量实验. 本文介绍该BPM系统的结构、作为系统核心部分的信号处理模块以及离线标定的实验结果和在线应用的实验结果, 表明该BPM系统具有不小于40dBm的动态范围, 不大于100μm的束流位置分辨率, 水平方向和垂直方向分别具有1.61dB/mm和1.51dB/mm的灵敏度. 校正铁强度与BPM读数关系的实验, 表明该BPM系统能正确地反映束流的位置变化情况, 并且确定了校正铁在水平方向和垂直方向的校正系数分别为0.46mm/A和0.58mm/A, 校正铁设置为默认值时该BPM处的束流中心水平位置和垂直位置分别为0.83mm和-0.57mm. 相似文献