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1.
许永红  石兰芳  莫嘉琪 《物理学报》2015,64(1):10201-010201
研究了在数学、力学中广泛出现的一类非线性强阻尼广义sine-Gordon扰动微分方程问题. 首先, 引入行波变换, 求出退化方程的精确解. 再构造一个泛函, 创建了一个变分迭代算法, 最后, 求出原非线性强阻尼广义sine-Gordon扰动微分方程问题的近似行波解析解. 用变分迭代法可得到的各次近似解, 具有便于求解、精度高等特点. 求得的近似解析解弥补了单纯用数值方法的模拟解的不足.  相似文献   

2.
对流占优扩散问题的高精度直线法   总被引:2,自引:1,他引:1  
吴雄华  谭志海 《计算物理》1999,16(2):211-216
基于常微分方程边值问题的高精度求解器SEVORD对偏微分方程作半离散,提出了求解一维对流扩散方程的高精度直线法,并采用局部一维化方法给出了求解二维对流扩散问题的高精度交替方向直线法。  相似文献   

3.
基于两重网格离散和区域分解技术,提出数值求解带阻尼项定常Navier-Stokes方程的三种并行两水平有限元算法。其基本思想是首先在粗网格上求解完全的非线性问题,以获得粗网格解,然后在重叠的局部细网格子区域上并行求解Stokes、 Oseen和Newton线性化的残差问题,最后在非重叠的局部细网格子区域上校正近似解。数值算例验证了算法的有效性。  相似文献   

4.
使用一种简化的准离散多重尺度法,研究了具有非线性基底势的一维离散非线性晶格的孤波解, 表明孤波能够在这种一维非线性晶格链中存在,而且非线性基底势对孤波的载波频率、群速度、振幅等动力学性质都将产生影响。 另一方面,我们还对非线性动力学方程进行了数值求解, 发现用简化的准离散多重尺度法得到的近似解与精确的计算机数值计算结果符合得较好。  相似文献   

5.
引入压力变量,将弹性力学控制方程表达为位移和压力的耦合偏微分方程组,采用重心插值近似未知量,利用重心插值微分矩阵得到平面问题控制方程的矩阵形式离散表达式.采用重心插值离散位移和应力边界条件,采用附加法施加边界条件,得到求解平面弹性问题的过约束线性代数方程组,采用最小二乘法求解过约束方程组,得到平面问题位移数值解.数值算例验证了所提方法的有效性和计算精度.  相似文献   

6.
杨沛  陈勇  李志斌 《物理学报》2010,59(6):3668-3673
将同伦分析法进行了推广,使之适用于求解离散修正KdV方程.获得了由指数函数表达的亮孤子解,该解析近似解与精确解符合很好.数值模拟结果说明了同伦分析法对求解复杂非线性问题的有效性和潜力.  相似文献   

7.
研究了微分方程对称分类在非线性偏微分方程组边值问题中的应用.首先,利用偏微分方程(组)完全对称分类微分特征列集算法确定了给定非线性偏微分方程组边值问题的完全对称分类;其次,利用一个扩充对称将非线性偏微分方程组边值问题约化为常微分方程组初值问题;最后,利用龙格-库塔法求解了常微分方程组初值问题的数值解.  相似文献   

8.
郑连存  冯志丰  张欣欣 《物理学报》2007,56(3):1549-1554
从理论上研究了一类广义扩散方程的求解问题. 利用相似变换和解析拆分技巧给出了求解该类非线性微分方程近似解的一种有效方法, 方程的解可以表示为一个收敛的幂级数. 近似解结果和数值结果非常符合,证明了所提出的方法的准确性和可靠性, 该方法可以用于解决其他科学和工程技术问题. 关键词: 广义扩散方程 非线性边界值问题 解析拆分 近似解析解  相似文献   

9.
为了解决复杂形状横截面的电磁波导问题,根据电磁波导的Hamilton体系,在辛几何形式下采用有限元半解析横向离散的方法对电磁波导进行求解.该方法可应用于任意各向异性材料,且便于处理不同介质的界面条件,求解用解析方法难以求解的复杂问题.利用棱单元进行有限元离散,给出矩形波导、T隔膜矩形波导、分层波导等多种波导的具体算例,其数值结果逼近于真实解,且伪解消除,表明该方法有效.  相似文献   

10.
非线性基底势对离散非线性晶格孤波动力学性质的影响   总被引:1,自引:0,他引:1  
使用一种简化的准离散多重尺度法,研究了具有非线性基底势的一维离散非线性晶格的孤波解,表明孤波能够在这种一维非线性晶格链中存在,而且非线性基底势对孤波的载波频率、群速度、振幅等动力学性质都将产生影响.另一方面,我们还对非线性动力学方程进行了数值求解,发现用简化的准离散多重尺度法得到的近似解与精确的计算机数值计算结果符合得...  相似文献   

11.
In this paper, we consider a numerical approximation for the boundary optimal control problem with the control constraint governed by a heat equation defined in a variable domain. For this variable domain problem, the boundary of the domain is moving and the shape of theboundary is defined by a known time-dependent function. By making use of the Galerkin finite element method, we first project the original optimal control problem into a semi-discrete optimal control problem governed by a system of ordinary differential equations. Then, based on the aforementioned semi-discrete problem, we apply the control parameterization method to obtain an optimal parameter selection problem governed by a lumped parameter system, which can be solved as a nonlinear optimization problem by a Sequential Quadratic Programming (SQP) algorithm. The numerical simulation is given to illustrate the effectiveness of our numerical approximation for the variable domain problem with the finite element method and the control parameterization method.  相似文献   

12.
张莹  徐伟  方同  徐旭林 《中国物理》2007,16(7):1923-1933
In this paper, the Chebyshev polynomial approximation is applied to the problem of stochastic period-doubling bifurcation of a stochastic Bonhoeffer-van der Pol (BVP for short) system with a bounded random parameter. In the analysis, the stochastic BVP system is transformed by the Chebyshev polynomial approximation into an equivalent deterministic system, whose response can be readily obtained by conventional numerical methods. In this way we have explored plenty of stochastic period-doubling bifurcation phenomena of the stochastic BVP system. The numerical simulations show that the behaviour of the stochastic period-doubling bifurcation in the stochastic BVP system is by and large similar to that in the deterministic mean-parameter BVP system, but there are still some featured differences between them. For example, in the stochastic dynamic system the period-doubling bifurcation point diffuses into a critical interval and the location of the critical interval shifts with the variation of intensity of the random parameter. The obtained results show that Chebyshev polynomial approximation is an effective approach to dynamical problems in some typical nonlinear systems with a bounded random parameter of an arch-like probability density function.  相似文献   

13.
陈建忠  史忠科 《计算物理》2006,23(3):273-280
对一维双曲型守恒律,给出了一种具有较小数值耗散的三阶半离散中心迎风格式.该格式以Liu和Tadmor提出的三阶无振荡重构为基础,同时考虑了波传播的单侧局部速度.时间离散用保持强稳定性的三阶Runge-Kutta方法.由于不需用Riemann解算器,避免了特征分解过程,保持了中心格式简单的优点.数值算例验证本方法可进一步减小数值耗散,提高分辨率.  相似文献   

14.
The applicability of the Dirichlet-to-Neumann technique coupled with finite difference methods is enhanced by extending it to multiple scattering from obstacles of arbitrary shape. The original boundary value problem (BVP) for the multiple scattering problem is reformulated as an interface BVP. A heterogenous medium with variable physical properties in the vicinity of the obstacles is considered. A rigorous proof of the equivalence between these two problems for smooth interfaces in two and three dimensions for any finite number of obstacles is given. The problem is written in terms of generalized curvilinear coordinates inside the computational region. Then, novel elliptic grids conforming to complex geometrical configurations of several two-dimensional obstacles are constructed and approximations of the scattered field supported by them are obtained. The numerical method developed is validated by comparing the approximate and exact far-field patterns for the scattering from two circular obstacles. In this case, for a second order finite difference scheme, a second order convergence of the numerical solution to the exact solution is easily verified.  相似文献   

15.
We present a high-order cell-centered Lagrangian scheme for solving the two-dimensional gas dynamics equations on unstructured meshes. A node-based discretization of the numerical fluxes for the physical conservation laws allows to derive a scheme that is compatible with the geometric conservation law (GCL). Fluxes are computed using a nodal solver which can be viewed as a two-dimensional extension of an approximate Riemann solver. The first-order scheme is conservative for momentum and total energy, and satisfies a local entropy inequality in its semi-discrete form. The two-dimensional high-order extension is constructed employing the generalized Riemann problem (GRP) in the acoustic approximation. Many numerical tests are presented in order to assess this new scheme. The results obtained for various representative configurations of one and two-dimensional compressible fluid flows show the robustness and the accuracy of our new scheme.  相似文献   

16.
间断有限元方法求解一维非平衡辐射扩散方程   总被引:2,自引:0,他引:2  
张荣培  蔚喜军  崔霞  冯涛 《计算物理》2012,29(5):641-646
研究一维非平衡辐射扩散方程的数值方法.通过求解间断系数热传导方程的广义黎曼问题,得到一种带加权数值流量,基于该数值流量构造了一类新型的间断有限元方法.在时间离散上采用向后Euler方法,形成的非线性方程组采用Picard迭代求解.数值试验表明该方法具有捕捉大梯度的能力,而且能适应扩散系数间断的情形.  相似文献   

17.
We study the numerical solution of the Fokker-Planck equation. This equation gives a good approximation to the radiative transport equation when scattering is peaked sharply in the forward direction which is the case for light propagation in tissues, for example. We derive first the numerical solution for the problem with constant coefficients. This numerical solution is constructed as an expansion in plane wave solutions. Then we extend that result to take into account coefficients that vary spatially. This extension leads to a coupled system of initial and final value problems. We solve this system iteratively. Numerical results show the utility of this method.  相似文献   

18.
杨秀丽  戴保东  张伟伟 《中国物理 B》2012,21(10):100208-100208
Based on the complex variable moving least-square(CVMLS) approximation and a local symmetric weak form,the complex variable meshless local Petrov-Galerkin(CVMLPG) method of solving two-dimensional potential problems is presented in this paper.In the present formulation,the trial function of a two-dimensional problem is formed with a one-dimensional basis function.The number of unknown coefficients in the trial function of the CVMLS approximation is less than that in the trial function of the moving least-square(MLS) approximation.The essential boundary conditions are imposed by the penalty method.The main advantage of this approach over the conventional meshless local Petrov-Galerkin(MLPG) method is its computational efficiency.Several numerical examples are presented to illustrate the implementation and performance of the present CVMLPG method.  相似文献   

19.
In this Letter, we employ finite element method to study a periodic initial value problem for the coupled Schrödinger-KdV equations. For the case of one dimension, this problem is reduced to a system of ordinary differential equations by using a semi-discrete scheme. The conservation properties of this scheme, the existence and uniqueness of the discrete solutions, and error estimates are presented. In numerical experiments, the resulting system of ordinary differential equations are solved by Runge-Kutta method at each time level. The superior accuracy of this scheme is shown by comparing the numerical solutions with the exact solutions.  相似文献   

20.
This paper analyzes well-posedness and stability of a conjugate heat transfer problem in one space dimension. We study a model problem for heat transfer between a fluid and a solid. The energy method is used to derive boundary and interface conditions that make the continuous problem well-posed and the semi-discrete problem stable. The numerical scheme is implemented using 2nd-, 3rd- and 4th-order finite difference operators on Summation-By-Parts (SBP) form. The boundary and interface conditions are implemented weakly. We investigate the spectrum of the spatial discretization to determine which type of coupling that gives attractive convergence properties. The rate of convergence is verified using the method of manufactured solutions.  相似文献   

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