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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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本文提出了一种用于FPGA中DDR SDRAM控制器的接口快速锁定的全数字延时锁定环。该电路对数据选择脉冲(DQS)实现90度的相位偏移。为了实现延时锁定环的快速锁定,同时解决了错误锁定的问题,本文提出了一种新颖的数字时间转换器的结构。在延时环路中设计了占空比纠正电路,实现50%的占空比输出。该延时锁定环电路采用0.13μm标准CMOS工艺设计制作。测试结果表明,工作频率范围为75MHz~350MHz,数字控制延时链(DCDL)的调节精度为15ps,并且电路的闭环特性能跟踪电压、温度等环境的变化。 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