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求解广义正则长波方程的守恒差分格式 总被引:3,自引:0,他引:3
本文对广义正则长波方程的初边值问题提出了—个隐式差分格式,该格式合理地模拟了方程本身所具有的两个守恒律.给出了差分解的先验估计,证明了差分解的唯一可解性、无条件收敛性及其稳定性. 相似文献
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基于截面经验似然方法,将双重广义线性模型的拟似然估计方程作为截面经验似然比函数的约束条件,构造了均值模型和散度模型未知参数的置信区间.最后通过数据模拟,将该方法与正态逼近方法比较,说明了该方法是有效和可行的. 相似文献
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电动力学电磁场边值问题的广义变分原理 总被引:1,自引:0,他引:1
给出了线性各项异性电磁场边值问题的广义虚功原理表达式,运用钱伟长教授提出的方法建立了该问题的广义变分原理,可直接反映该问题的全部特征,即4个Maxwell方程、2个场强-位势方程、2个本构方程和8个边界条件.继而导出了一族有先决条件的广义变分原理.作为例证,导出了两个退化形式的广义变分原理,和已知的广义变分原理等价.此外还导出了两个修正的广义变分原理,可为该问题提供杂交有限元模型.建立的各广义变分原理可为电磁场边值问题的有限元应用提供更为完善的理论基础. 相似文献
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Navier-Stokes方程的全离散Jacobi-球面调和谱方法 总被引:2,自引:0,他引:2
提出了一种用于球内Navier-Stokes方程的全离散Jacobi-球面调和谱方法,并证明了它的广义稳定性和收敛性.数值结果表明了该方法的有效性.该方法也可应用于球形区域中的其它问题. 相似文献
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用微分形式的吴方法讨论了广义KdV—Burgers方程不同系数情况下的势对称,并且利用这些对称求得了相应的不变解,这些解对进一步研究广义KdV—Burgers方程所描述的物理现象具有重要意义. 相似文献
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利用孤立子方程KdV-mKdV的朗斯基解的形式和结构,我们提出了朗斯基形式展开法,运用这一方法获得了KdV-mKdV方程的丰富的新的复合函数解,并且朗斯基行列式中的元素不满足任何线性偏微分方程组.所得到的复合函数解是使用其它的方法得不到的. 相似文献
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Conclusion The approach demonstrated in [1] for deducing generalized rod models from equations for uniform and isotropic folded structures in which the strips are rigidly joined in bending was expanded to the case of symmetrical anisotropic structures. Thus, we have developed an effective approach for global structural analysis of thin-walled three-dimensional structures made of composites. Here, we examined the feasibility of using the method of initial parameters to solve the differential equations in certain special cases. In the general case, global structural analysis requires the use of powerful numerical methods. In the case of an isotropic material, use can be made of methods of solving first-order canonical differential equations or methods based on a solution obtained by means of quasi-unidimensional finite elements. The application of the last approach to the case of composite materials will be demonstrated in a future article.Translated from Mekhanika Kompozitnykh Materialov, No. 4, pp. 641–649, July–August, 1989. 相似文献
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Generalized method and its application in the higher-order nonlinear Schrodinger equation in nonlinear optical fibres 总被引:8,自引:0,他引:8
A generalized method, which is called the generally projective Riccati equation method, is presented to find more exact solutions of nonlinear differential equations based upon a coupled Riccati equation. As an application of the method, we choose the higher-order nonlinear Schrodinger equation to illustrate the method. As a result more new exact travelling wave solutions are found which include bright soliton solutions, dark soliton solution, new solitary waves, periodic solutions and rational solutions. The new method can be extended to other nonlinear differential equations in mathematical physics. 相似文献
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If the system of linear equations defining a multivariate rational interpolant is singular, then the table of multivariate rational interpolants displays a structure where the basic building block is a hexagon. Remember that for univariate rational interpolation the structure is built by joining squares. In this paper we associate with every entry of the table of rational interpolants a well-defined determinant representation, also when this entry has a nonunique solution. These determinant formulas are crucial if one wants to develop a recursive computation scheme.In section 2 we repeat the determinant representation for nondegenerate solutions (nonsingular systems of interpolation conditions). In theorem 1 this is generalized to an isolated hexagon in the table. In theorem 2 the existence of such a determinant formula is proven for each entry in the table. We conclude with an example in section 5. 相似文献
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We introduce an orthogonal system on the half line, induced by generalized Jacobi functions. Some basic results on the generalized Jacobi rational approximation are established, which play important roles in the related spectral method. As an example of applications, the rational spectral method is proposed for partial differential equations of degenerate type. Its convergence is proved. Numerical results demonstrate its efficiency. 相似文献
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A boundary-discontinuous Fourier expansion method to analyze the displacements and stresses in cross-ply composite laminates
with transverse cracks is presented. The governing equations of the problem are derived on the basis of the generalized plane
strain assumption and two-dimensional equations of elasticity. By employing the boundary-discontinuous Fourier expansion method,
the governing equations in the form of coupled high-order ODEs are transformed to a set of systems of linear algebraic equations.
The method is used to obtain solutions for which published results can be found for comparisons. Compared with the conventional
numerical methods for solving coupled high-order ODEs, the method presented is more efficient. Further parametric studies
are carried out for cracked laminates with various geometric and material properties.
Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 6, pp. 795–826, November–December, 2008. 相似文献
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In the present paper, some types of general solutions of a first-order nonlinear ordinary differential equation with six degree are given and a new generalized algebra method is presented to find more exact solutions of nonlinear differential equations. As an application of the method and the solutions of this equation, we choose the (2 + 1) dimensional Boiti Leon Pempinelli equation to illustrate the validity and advantages of the method. As a consequence, more new types and general solutions are found which include rational solutions and irrational solutions and so on. The new method can also be applied to other nonlinear differential equations in mathematical physics. 相似文献
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Based on symbolic computation and the idea of rational expansion method, a new generalized compound Riccati equations rational expansion method (GCRERE) is suggested to construct a series of exact complexiton solutions for nonlinear evolution equations. Compared with most existing rational expansion methods and other sophisticated methods, the proposed method not only recover some known solutions, but also find some new and general complexiton solutions. The validity and reliability of the method is tested by its application to the (2+1)-dimensional Burgers equation. It is shown that more complexiton solutions can be found by this new method. 相似文献
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Using the variational method, a system of resolving equations and boundary conditions is deduced on the basis of the nonclassical model for a composite bar. The order of the equations depends on the step of the iterative process. For normal and tangential loads, these equations are realized in trigonometric series. The results are presented as a sum of the classical solution and an additional part, which is determined by the influence of the shear deplanation of cross sections and is taken into account by higher iterations. The problems for bars with various cross section variants are considered. 相似文献
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This paper is concerned with a generalization of a functional differential equation known as the pantograph equation which contains a linear functional argument. In this article, a new spectral collocation method is applied to solve the generalized pantograph equation with variable coefficients on a semi-infinite domain. This method is based on Jacobi rational functions and Gauss quadrature integration. The Jacobi rational-Gauss method reduces solving the generalized pantograph equation to a system of algebraic equations. Reasonable numerical results are obtained by selecting few Jacobi rational–Gauss collocation points. The proposed Jacobi rational–Gauss method is favorably compared with other methods. Numerical results demonstrate its accuracy, efficiency, and versatility on the half-line. 相似文献
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Motivated by Sasaki’s work on the extended Hensel construction for solving multivariate algebraic equations, we present a generalized Hensel lifting, which takes advantage of sparsity, for factoring bivariate polynomial over the rational number field. Another feature of the factorization algorithm presented in this article is a new recombination method, which can solve the extraneous factor problem before lifting based on numerical linear algebra. Both theoretical analysis and experimental data show that the algorithm is efficient, especially for sparse bivariate polynomials. 相似文献