共查询到20条相似文献,搜索用时 31 毫秒
1.
Abdul Ghafoor Sirajul Haq Manzoor Hussain Thabet Abdeljawad Manar A. Alqudah 《Entropy (Basel, Switzerland)》2022,24(4)
In this work, an efficient and robust numerical scheme is proposed to solve the variable coefficients’ fourth-order partial differential equations (FOPDEs) that arise in Euler–Bernoulli beam models. When partial differential equations (PDEs) are of higher order and invoke variable coefficients, then the numerical solution is quite a tedious and challenging problem, which is our main concern in this paper. The current scheme is hybrid in nature in which the second-order finite difference is used for temporal discretization, while spatial derivatives and solutions are approximated via the Haar wavelet. Next, the integration and Haar matrices are used to convert partial differential equations (PDEs) to the system of linear equations, which can be handled easily. Besides this, we derive the theoretical result for stability via the Lax–Richtmyer criterion and verify it computationally. Moreover, we address the computational convergence rate, which is near order two. Several test problems are given to measure the accuracy of the suggested scheme. Computations validate that the present scheme works well for such problems. The calculated results are also compared with the earlier work and the exact solutions. The comparison shows that the outcomes are in good agreement with both the exact solutions and the available results in the literature. 相似文献
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针对核反应堆安全工程对某些数值计算结果要求较高的精度和正的误差, 以及舰船核反应堆机动性对计算速度的要求, 需要从数学上寻找一种新的数值计算方法, 以满足实际曲线向上凸或向下凹时计算值总是略高于真实值, 且误差不大于欧拉法和改进的欧拉法所得值. 本文研究曲率权重法求解点堆中子动力学方程组, 该方法是在曲率圆法的基础上引入权重的思想来衡量间隔步长上两个曲率对该步长曲率平均值的贡献. 与欧拉法和改进的欧拉法比较, 曲率权重法的计算结果总是能够高于真实值或有正的误差, 且精度和计算速度得到明显提升. 将该方法用于次临界堆阶跃和线性引入反应性时中子密度的求解, 能够快速得到满足计算要求和高精度的数值结果. 相似文献
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《Journal of sound and vibration》1996,196(4):407-427
The vibration and the acoustic radiation of a baffled rectangular plate in contact with a dense fluid is considered. By using Green's representation theorem, the original system of differential equations governing both the displacement and the acoustic sound pressure is transformed into a system of coupled boundary integral equations. The unknown functions (the displacement of the plate, the pressure jump at the surface of the plate and the boundary sources) are expanded as series of Tchebycheff polynomials. The new unknowns (the coefficients of the series) are calculated by using a collocation method. Some results, both theoretical and numerical, are given concerning the resolution properties of the Tchebycheff approximation. The numerical difficulties are presented, and solutions of these are proposed. Numerical examples are given. 相似文献
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应用计算全息制作的子波匹配滤波器实现光学子波变换的研究 总被引:6,自引:0,他引:6
介绍了一种应用计算全息制作的子波匹配滤波器实现光学子波变换的新方法,应用计算全息制作Haar子波函数的匹配滤波器和光学Vander Lugt相关器实现了二维子波变换,给出了实验结果。这种方法可实现任意子波函数的光学子波变换,且简单易行。 相似文献
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《Journal of computational physics》2006,211(1):1-8
A numerical scheme based on the method of fundamental solutions (MFS) is proposed for the solution of 2D and 3D Stokes equations. The fundamental solutions of the Stokes equations, Stokeslets, are adopted as the sources to obtain flow field solutions. The present method is validated through other numerical schemes for lid-driven flows in a square cavity and a cubic cavity. Test results obtained for a rectangular cavity with wave-shaped bottom indicate that the MFS is computationally efficient than the finite element method (FEM) in dealing with irregular shaped domain. The paper also discusses the effects of number of source points and their locations on the numerical accuracy. 相似文献
6.
提出了一种新的恒星大气物理参数自动估计的新方案,并称之为SVR(Haar)。由于观测光谱受到大量宇宙辐射、大气和观测设备等引起的噪声干扰,且这种噪声干扰往往是其中的频率较高成分。所以该方案的基本思想是首先使用Haar小波剔除高频噪声成份,以提高恒星大气物理参数估计的准确性;然后使用支持向量机回归方法(SVR)对恒星参数做出估计,该方法能通过ε不敏感域进一步提高对光谱微小畸变和干扰的容许能力,增强解决方案的鲁棒性。为了验证SVR(Haar)方案的有效性,针对相关研究中的权威模拟恒星光谱和SLOAN发布的实测光谱,以及文献中的典型处理方法,做了大量比较实验。实验结果表明,所提出的SVR(Haar)恒星参数估计方案比文献中常用的主成分分析和非参数回归模型均要好。 相似文献
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Non—equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method 总被引:35,自引:0,他引:35
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In this paper, we propose a new approach to implementing boundary conditions in the lattice Boltzmann method (LBM). The basic idea is to decompose the distribution function at the boundary node into its equilibrium and non-equilibrium parts, and then to approximate the non-equilibrium part with a first-order extrapolation of the non-equilibrium part of the distribution at the neighbouring fluid node. Schemes for velocity and pressure boundary conditions are constructed based on this method. The resulting schemes are of second-order accuracy. Numerical tests show that the numerical solutions of the LBM together with the present boundary schemes are in excellent agreement with the analytical solutions. Second-order convergence is also verified from the results. It is also found that the numerical stability of the present schemes is much better than that of the original extrapolation schemes proposed by Chen et al. (1996 Phys. Fluids 8 2527). 相似文献
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A new lattice Bhatnagar--Gross--Krook (LBGK) model for a class of the generalized
Burgers equations is proposed. It is a general LBGK model for nonlinear Burgers
equations with source term in arbitrary dimensional space. The linear stability of
the model is also studied. The model is numerically tested for three problems in
different dimensional space, and the numerical results are compared with either
analytic solutions or numerical results obtained by other methods. Satisfactory
results are obtained by the numerical simulations. 相似文献
12.
This paper presents three-dimensional free vibration analysis of isotropic rectangular plates with any thicknesses and arbitrary boundary conditions using the B-spline Ritz method based on the theory of elasticity. The proposed method is formulated by the Ritz procedure with a triplicate series of B-spline functions as amplitude displacement components. The geometric boundary conditions are numerically satisfied by the method of artificial spring. To demonstrate the convergence and accuracy of the present method, several examples with various boundary conditions are solved, and the results are compared with other published solutions by exact and other numerical methods based on the theory of elasticity and various plate theories. Rapid, stable convergences as well as high accuracy are obtained by the present method. The effects of geometric parameters on the vibrational behavior of cantilevered rectangular plates are also investigated. The results reported here may serve as benchmark data for finite element solutions and future developments in numerical methods. 相似文献
13.
Stochastic response of van der Pol oscillator with two kinds of fractional derivatives under Gaussian white noise excitation
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This paper aims to investigate the stochastic response of the van der Pol(VDP) oscillator with two kinds of fractional derivatives under Gaussian white noise excitation.First,the fractional VDP oscillator is replaced by an equivalent VDP oscillator without fractional derivative terms by using the generalized harmonic balance technique.Then,the stochastic averaging method is applied to the equivalent VDP oscillator to obtain the analytical solution.Finally,the analytical solutions are validated by numerical results from the Monte Carlo simulation of the original fractional VDP oscillator.The numerical results not only demonstrate the accuracy of the proposed approach but also show that the fractional order,the fractional coefficient and the intensity of Gaussian white noise play important roles in the responses of the fractional VDP oscillator.An interesting phenomenon we found is that the effects of the fractional order of two kinds of fractional derivative items on the fractional stochastic systems are totally contrary. 相似文献
14.
REN XueZao LIAO Xu LI Lei & WANG KeLin School of Science Southwest University of Science Technology Mian Yang China 《中国科学:物理学 力学 天文学(英文版)》2010,(1)
A new approach-the method of coherent state orthogonal expansion is developed for one-dimensional Holstein model. In zeroth order approximation, the formula of ground state energy is deduced analytically and the solutions in strong- and weak-coupling limits are obtained correctly. When the trial wave-function of ground state is expanded to the second order, the obtained ground state energy agrees quite well with that calculated by numerical method in all coupling regimes. The present approach can be easily ... 相似文献
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An extended Fan's algebraic method is used for constructing exact traveling wave solution of nonlinear partial differential equations. The key idea of this method is to introduce an auxiliary ordinary differential equation which is regarded as an extended elliptic equation and
whose degree r is expanded to the case of r>4. The efficiency of the
method is demonstrated by the KdV equation and the variant Boussinesq
equations. The results indicate that the method not only offers all
solutions obtained by using Fu's and Fan's methods, but also some new solutions. 相似文献
16.
提出了一种新的水平变化波导中声场的耦合简正波求解方法,该方法能够处理二维点源和线源问题,提供声场的双向解。该方法利用全局矩阵(DGM)一次性求解耦合模式的系数,消除了传播矩阵递推求解中存在的误差累积问题;此外,改善了现有模型中对距离函数的归一化方法,从而避免了泄露模式指数增长导致的数值溢出问题。本文还给出了绝对软海底理想波导中耦合矩阵的闭合表达式,并分析了单个阶梯下简正波耦合现象。此外,本文还计算了理想楔形波导中的声传播问题(ASA标准问题),并与解析解及COUPLE07计算结果进行了比较,结果表明该方法是一种稳定、精确的水平变化波导中的声场计算方法。 相似文献
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S.W. KANGJ.M. LEE 《Journal of sound and vibration》2002,251(3):505-517
The natural frequencies and mode shapes of a composite rectangular membrane with no exact solutions are found by using an analytical method appropriate for the geometric feature of the title problem membrane presented here. The method has a key feature in which the theoretical development is very simple and only a small amount of numerical calculation is required. Example studies show that the natural frequencies and their associated modes obtained from the method are found to be very accurate compared with the results by the FEM (SYSNOISE) or exact solutions. Furthermore, the natural frequencies converge rapidly and accurately to the exact values or the numerical results obtained from the finite element model using meshes sufficient to yield already converging natural frequencies, even when a small number of series functions are used in the proposed method. 相似文献
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考虑二次梯度项影响的双渗模型的动态特征 总被引:10,自引:1,他引:9
在传统试井模型的非线性偏微分方程中根据弱可压缩液体的假设忽略了二次梯度项,已经知道在试井较长时间忽略二次梯度项将产生误差,故对于双重介质流动系统保留了非线性偏微分方程中的二次梯度项,建立了双渗流动模型.采用Douglas-Jones预估校正法获得了无限大地层定产量生产时和定压生产时双渗模型的数值解,分别讨论了液体压缩系数和双重介质参数变化时压力变化规律,做出了典型压力曲线图版,这些结果可用于实际试井分析. 相似文献
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A Laplace decomposition algorithm is adopted to investigate numerical solutions of a class of nonlinear partial differential equations with nonlinear term of any order, utt + auxx + bu + cup + du^2p-1 = 0, which contains some important equations of mathematical physics. Three distinct initial conditions are constructed and generalized numerical solutions are thereby obtained, including numerical hyperbolic function solutions and doubly periodic ones. Illustrative figures and comparisons between the numerical and exact solutions with different values of p are used to test the efficiency of the proposed method, which shows good results are azhieved. 相似文献