共查询到20条相似文献,搜索用时 203 毫秒
1.
2.
3.
非线性发展方程的小模板简化Pade格式 总被引:1,自引:1,他引:0
在有理逼近的紧致格式的理论基础上,采用特别的统一的Pade逼近形式,构造了针对高阶非线性发展方程的、简单小模板的差商格式.不仅保持了格式的四阶精度,而且还可以采用追赶法求解得到的3对角矩阵,或者采用三阶Runge-Kuna法直接求解积分.计算效果通过多种算例表明是十分令人满意的.相对于其他差分格式,此方法具有模板较小而精度保持四阶的优点. 相似文献
4.
本文研究一类二维非线性的广义sine-Gordon(简称SG)方程的有限差分格式.首先构造三层时间的紧致交替方向隐式差分格式,并用能量分析法证明格式具有二阶时间精度和四阶空间精度.然后应用改进的Richardson外推算法将时间精度提高到四阶.最后,数值算例证实改进后的算法在空间和时间上均达到四阶精度. 相似文献
5.
一类min-max-min问题的区间算法 总被引:4,自引:0,他引:4
讨论了一类由一阶连续可微函数构成的无约束min-max-min问题.通过构造目标函数的区间扩张、无解区域删除原则,建立了求解min-max-min问题的区间算法,证明了算法的收敛性,给出了数值算例.理论证明和数值结果表明方法是可靠和有效的. 相似文献
6.
本文将正交校正共轭梯度法推广来解只有部分变量带非负约束而其它变量无约束的严格凸二次规划,所建立的新算法的优点是:在迭代过程中,不用求逆矩阵,这样能保持矩阵的稀疏性,数值结果表明:算法对大规模稀疏二次规划问题是可行和有效的. 相似文献
7.
给出了交替方向的二维扩散方程的精细积分算法,将一个时间步积分分为两个方向,使大规模矩阵的计算转化为一些小矩阵的计算,减小了每一步求解的计算量.对于方形区域的齐次方程,计算结果与全城精细积分完全相同,而计算量和存储量都要小得多.算例表明了算法具有较高的并行计算加速比和计算效率. 相似文献
8.
《数学的实践与认识》2017,(20)
提出了数值求解三维热传导方程的一个四阶精度的有限差分格式,首先对三个空间方向上的二阶导数项,采用四次样条函数来近似,从而得到半离散的常微分方程.然后利用常微分方程的解析解表达式,时间矩阵利用Padé近似,得到时间和空间均为四阶精度的差分格式.最后利用方法计算了两个数值算例,并与文献中结果进行了对比,从而验证了高精度格式的性能. 相似文献
9.
对用于求解非线性发展方程的两个带变时间步的两重网格算法,对空间变量用有限元离散,对时间变量分别用一阶精度Euler显式和二阶精度半隐式差分格式离散,然后构造两重网格算法,通过深入的稳定性分析,得出本文的算法优于标准全离散有限元算法。 相似文献
10.
Winograd矩阵乘法算法用于任意阶矩阵时的一种新处理方法 总被引:3,自引:0,他引:3
摘要t矩阵乘法StraSsen算法及其变形winograd算法用分而治之的方法把矩阵乘法时间复杂性由传统的D(n。)改进到0(佗kg。n.但是对于奇数阶矩阵,在划分子矩阵时,要作特殊处理才能继续使用此算法.本文提出了一种非等阶“十”字架划分方法,可以最少化填零,最大化性能,使得奇数阶矩阵乘法的时间复杂性更加接近偶数阶矩阵乘法的效果.计算实例显示该方法是有效的. 相似文献
11.
曾文平 《高等学校计算数学学报》2004,26(4):378-384
In this paper, we present two classes of symplectic schemes with high order accuracy for solving four-order rod vibration equation utt uxxxx=0 via the third type generating function method. First, the equation of four order rod vibration is written into the canonical Hamilton system; second, overcoming successfully the essential difficult on the calculus of high order variations derivative, we get the semi-discretization with arbitrary order of accuracy in time direction for the PDEs by the third type generating function method. Furthermore the discretization of the related modified equation of original equation is obtained. Finally, arbitrary order accuracy symplectic schemes are obtained. Numerical results are also presented to show the effectiveness of the scheme, high order accuracy and properties of excellent long-time numerical behavior. 相似文献
12.
Numerical computation of branch points in nonlinear equations 总被引:1,自引:0,他引:1
Rüdiger Seydel 《Numerische Mathematik》1979,33(3):339-352
Summary The numerical computation of branch points in systems of nonlinear equations is considered. A direct method is presented which requires the solution of one equation only. The branch points are indicated by suitable testfunctions. Numerical results of three examples are given. 相似文献
13.
《Journal of Computational and Applied Mathematics》2001,135(1):63-78
A definition of connection coefficients is introduced and techniques of computation are presented. We use semi-implicit time difference scheme to solve Burgers equation by applying the evaluations of connection coefficients in calculating the integrals of the variational form. Comparisons of accuracy and robustness of numerical solutions are mentioned in the examples. 相似文献
14.
Xiu Yang Xiaoyun Jiang Hui Zhang 《Mathematical Methods in the Applied Sciences》2019,42(18):6475-6489
The object of this paper is to present the numerical solution of the time‐space fractional telegraph equation. The proposed method is based on the finite difference scheme in temporal direction and Fourier spectral method in spatial direction. The fast Fourier transform (FFT) technique is applied to practical computation. The stability and convergence analysis are strictly proven, which shows that this method is stable and convergent with (2?α) order accuracy in time and spectral accuracy in space. Moreover, the Levenberg‐Marquardt (L‐M) iterative method is employed for the parameter estimation. Finally, some numerical examples are given to confirm the theoretical analysis. 相似文献
15.
Jincun Liu 《Numerical Functional Analysis & Optimization》2013,34(15):1635-1655
AbstractIn this paper, a Crank–Nicolson finite difference/finite element method is considered to obtain the numerical solution for a time fractional Sobolev equation. Firstly, the classical finite element method is presented. Stability and error estimation for the fully discrete scheme are rigorously established. However, the amount of calculation and computing time are too large due to many degrees of freedom of classical finite element scheme and nonlocality of fractional differential operator. And then the modified reduced-order finite element scheme with low dimensions and sufficiently high accuracy, which is based on proper orthogonal decomposition technique, is provided. Stability and convergence for the reduced-order scheme are also studied. At last, numerical examples show that the results of numerical computation are consistent with previous theoretical conclusions. 相似文献
16.
17.
Wenyuan Liao 《Numerical Methods for Partial Differential Equations》2013,29(3):778-798
In this article, we extend the fourth‐order compact boundary scheme in Liao et al. (Numer Methods Partial Differential Equations 18 (2002), 340–354) to a 3D problem and then combine it with the fourth‐order compact alternating direction implicit (ADI) method in Gu et al. (J Comput Appl Math 155 (2003), 1–17) to solve the 3D reaction‐diffusion equation with Neumann boundary condition. First, the reaction‐diffusion equation is solved with a compact fourth‐order finite difference method based on the Padé approximation, which is then combined with the ADI method and a fourth‐order compact scheme to approximate the Neumann boundary condition, to obtain fourth order accuracy in space. The accuracy in the temporal dimension is improved to fourth order by applying the Richardson extrapolation technique, although the unconditional stability of the numerical method is proved, and several numerical examples are presented to demonstrate the accuracy and efficiency of the proposed new algorithm. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 相似文献
18.
四阶杆振动方程的一族高稳定的十字架格式 总被引:1,自引:0,他引:1
用辛几何的观点得到了四阶杆振动方程的一族十字架辛格式,对于四阶杆振动方程的稳定条件不一定随时间方向的精度的提高而放宽,而随空间方向精度的提高稳定范围缩小.数值例子表明单辛算法具有良好的数值稳定性. 相似文献
19.
This paper presents a computational technique for Fredholm integral equation of the second kind and Volterra integral equation of the second kind. The method is based upon Haar functions approximation. Properties of Rationalized Haar functions are first presented, the operational matrix of integration together with product operational matrix and Newton–Cotes nodes are utilized to reduce the computation of integral equations into some algebraic equations. The method is computationally attractive and applications are demonstrated through illustrative examples. 相似文献
20.
F. G. Tcheremissine 《Computational Mathematics and Mathematical Physics》2012,52(2):252-268
A method is proposed for computing the collision operator of a generalized Boltzmann kinetic equation with allowance for energy
transfer from translational to vibrational or rotational degrees of freedom. The collision operator is computed using a projection
method on a uniform velocity grid. The operator satisfies the mass, momentum, and energy conservation laws and vanishes for
an equilibrium velocity distribution function. Approximate models are suggested that provide savings on the computation of
rotational-translational relaxation. Numerical examples are presented. 相似文献