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1.
非线性非完整系统Vacco动力学方程的积分方法   总被引:3,自引:0,他引:3  
本文给出积分非线性非完整系统Vacco动力学方程的积分方法。首先,将Vacco动力学方程表示为正则形式和场方程形式:然后,分别用梯度法,单分量法和场方法积分相应完整系统的动力学方程,并加上非完整约束对初条件的限制而得到非线性非完整系统Vacco动力学方程的解.  相似文献   

2.
本文给出数值方法解Volterra积分方程的稳定性分析,我们判定可约积分方法的数值稳定性基于如下试验方程其中,是正常数,p和q是复值的。在上述试验方程的情况下,我们研究θ-方法及可约积分方法的稳定性。  相似文献   

3.
对于径向变形的压电空心圆柱和空心球弹性动力学问题,丁皓江等最近的研究表明,可以将它转变为关于一个时间函数的第二类Volterra积分方程,使求解工作得到极大的简化,又使探索第二类Volterra积分方程的快速而又高精度的数值解法成为一个关键.采用插值逼近方法,成功地导出了两个新型的递推公式,不仅计算速度快,且在较大时间步长时仍具有足够的精度,有着广泛的应用价值。  相似文献   

4.
胡齐芽 《计算数学》1998,20(3):261-266
1.引言由于对积分算子方程来说,配置法比Galerkin法具计算量小的优点(少算一重积分),故配置法更受人们重视.但已有的文献几乎都是将配置空间取作非连续的分片多项式样条空间,以得到某种超收敛结果(如[1,2]).这种方法存在下列不足:(a)光滑核Volterra积分方程与光滑核Fredholm积分方程具完全不同的收敛性质[1],且需用不同的方法获得其加速收敛结果(比较[31与[4]),尽管Volterra积分方程在理论上被看作是Fredholm积分方程的特殊情形;(b)光滑核Volterra积分方程的配置解不具任何超收敛性,其迭代配置解也只在结点…  相似文献   

5.
吕涛  黄晋 《应用数学学报》2001,24(3):321-332
借助位势理论,平面双调和方程的Dirichlet问题被转化为第一类边界积分方程组,本文使用新型的反常积分的求积公式构造出解造解此类边界积分方程的机械求积方法,证明了该方法具有O(h^3)阶精度和误差的h^3幂渐近展开,故借助Richardson外推还能提高精度阶。  相似文献   

6.
非对称载荷作用的外部圆形裂纹问题   总被引:2,自引:2,他引:0  
使用边界积分方程方法,研究了三维无限弹性体中受非对称载荷作用的外部圆形裂纹问题。通过使用Fourier级数和超几何函数,将问题的二维边界奇异积分方程简化为Abel型方程,获得了一般非对称载荷作用的外部圆形裂纹问题的应力强度因子精确解,比用Hankel变换法得到的结果更为一般。结果表明:边界积分方程法在解析分析方面还有很大的潜力。  相似文献   

7.
石军  林群 《应用数学学报》1995,18(2):193-201
本文对于一类具非光滑核第二类Fredholm方程的Collocation解提出一种迭代一校正方法,使得在计算量增加很少的前提下,成倍提高逼近解精度,并将此方法用于平面角域上边界积分方程,从而给出了其相应微分方程逼近解的高精度算法,此方法还是一种自适应方法。  相似文献   

8.
关于薄板的无网格局部边界积分方程方法中的友解   总被引:3,自引:1,他引:2  
无网格局部边界积分方程方法是最近发展起来的一种新的数值方法,这种方法综合了伽辽金有限元、边界元和无单元伽辽金法的优点,是一种具有广阔应用前景的、真正的无网格方法.把无网格局部边界积分方程方法应用于求解薄板问题,给出了薄板无网格局部边界积分方程方法所需要的友解及其全部公式.  相似文献   

9.
二维Fredholm积分方程Nystrom方法的渐近展开及其外推   总被引:1,自引:0,他引:1  
本文讨论了求解二维第二类Fredholm积分方程的Nystrom方法,得到了数值解的逐项渐近展开,从而可进行Richardson外推,提高数值解的精度。  相似文献   

10.
二维Volterra积分方程数值解的渐近展开及其外推   总被引:1,自引:1,他引:0  
本文讨论了求解二维Volterra积分方程的Nystrom方法,得到了数值解的逐项渐近展开,从而可进行Richardson外推,提高数值解的精度。  相似文献   

11.
An initial-value method of Bownds for solving Volterra integral equations is reexamined using a variable-step integrator to solve the differential equations. It is shown that such equations may be easily solved to an accuracy ofO(10–8), the error depending essentially on that incurred in truncating expansions of the kernel to a degenerate one.This work was sponsored by a University of Nevada at Las Vegas Research Grant.  相似文献   

12.
The meshless local Petrov–Galerkin (MLPG) method is employed for anisotropic transient thermoelasticity analysis of 2D decagonal quasicrystals (QCs) subjected to transient thermal and mechanical shock loadings. The wave type model and the elasto-hydrodynamic model are applied to derive the phonon and phason governing equations, respectively. The temperature affects only the phonon field. To find the temperature distributions on the assumed 2D domain, the anisotropic heat conduction problem is solved using the MLPG method. Also, the MLPG method is successfully employed to obtain the transient behaviors of both phonon and phason displacements by solving the governing equations in local integral equations (LIEs) forms. Making use a unit step function as the test functions in the local weak-form of governing equations, we derived the local integral equations (LIEs) considered on small subdomains identical with support domains of test functions around each node. The radial basis functions are used for approximation of the spatial variation of field variables. The Laplace-transform technique is utilized to discretize the time variations.  相似文献   

13.
We introduce a hybrid Gegenbauer (ultraspherical) integration method (HGIM) for solving boundary value problems (BVPs), integral and integro-differential equations. The proposed approach recasts the original problems into their integral formulations, which are then discretized into linear systems of algebraic equations using Gegenbauer integration matrices (GIMs). The resulting linear systems are well-conditioned and can be easily solved using standard linear system solvers. A study on the error bounds of the proposed method is presented, and the spectral convergence is proven for two-point BVPs (TPBVPs). Comparisons with other competitive methods in the recent literature are included. The proposed method results in an efficient algorithm, and spectral accuracy is verified using eight test examples addressing the aforementioned classes of problems. The proposed method can be applied on a broad range of mathematical problems while producing highly accurate results. The developed numerical scheme provides a viable alternative to other solution methods when high-order approximations are required using only a relatively small number of solution nodes.  相似文献   

14.
横观各向同性电磁弹性介质中裂纹对SH波的散射   总被引:2,自引:0,他引:2  
研究横观各向同性电磁弹性介质中裂纹和反平面剪切波之间的相互作用.根据电磁弹性介质的平衡运动微分方程、电位移和磁感应强度微分方程,得到SH波传播的控制场方程.引入线性变换,将控制场方程简化为Helmholtz方程和两个Laplace方程.通过Fourier变换,并采用非电磁渗透型裂面边界条件.得到了柯西奇异积分方程组.利用Chebyshev多项式求解积分方程.得到应力场、电场和磁场以及动应力强度因子的表达,并给出了数值算例.  相似文献   

15.
The semi-inverse method is adopted to search for a variational principle for an unelectroded piezoelastic beam. A trial variational formulation with energy integral is constructed with an unknown function, which is identified so that the Euler–Lagrange equations are equivalent to the governing equations.  相似文献   

16.
研究形如的模糊Volterra积分方程整体解的存在性.这里h,k,g是实值函数,f为强模糊Henstock可积的模糊数值函数.所用的方法和工具是利用模糊数值函数的等度可积性和非紧性测度的性质以及广义Darbo不动点定理.  相似文献   

17.
In this paper, a novel meshless technique termed the random integral quadrature (RIQ) method is developed for the numerical solution of the second kind of the Volterra integral equations. The RIQ method is based on the generalized integral quadrature (GIQ) technique, and associated with the Kriging interpolation function, such that it is regarded as an extension of the GIQ technique. In the GIQ method, the regular computational domain is required, in which the field nodes are scattered along straight lines. In the RIQ method however, the field nodes can be distributed either uniformly or randomly. This is achieved by discretizing the governing integral equation with the GIQ method over a set of virtual nodes that lies along straight lines, and then interpolating the function values at the virtual nodes over all the field nodes which are scattered either randomly or uniformly. In such a way, the governing integral equation is converted approximately into a system of linear algebraic equations, which can be easily solved.  相似文献   

18.
A substantial number of new indefinite integrals involving the incomplete elliptic integral of the third kind are presented, together with a few integrals for the other two kinds of incomplete elliptic integral. These have been derived using a Lagrangian method which is based on the differential equations which these functions satisfy. Techniques for obtaining new integrals are discussed, together with transformations of the governing differential equations. Integrals involving products combining elliptic integrals of different kinds are also presented.  相似文献   

19.
This study investigates the accuracy of nonlinear vibration analyses of a suspended cable, which possesses quadratic and cubic nonlinearities, with one-to-one internal resonance. To this end, we derive approximate solutions for primary resonance using two different approaches. In the first approach, the method of multiple scales is directly applied to governing equations, which are nonlinear partial differential equations. In the second approach, we first discretize the governing equations by using Galerkin’s procedure and then apply the shooting method. The accuracy of the results obtained by these approaches is confirmed by comparing them with results obtained by the finite difference method.  相似文献   

20.
This paper presents an integral equation formulation and its discretization scheme for the elastodynamic problem in which the material properties are prescribed as arbitrary, continuous and differentiable functions of the spatial coordinates. The formulation is made by using the Green's function for the corresponding problem in homogenous elasticity. From a weighted residual statement of the problem, the governing differential equation is transformed into a set of the integral equations in the inner domain as well as on the boundary. These integral equations are discretized by introducing a finite number of the boundary-volume-time elements, and the solution for the system of linear equations thus obtained is discussed.  相似文献   

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