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线性代数方程组正交化行处理法 总被引:6,自引:1,他引:5
给出了一种结合正交化方法和行处理法求解n阶非奇异线性代数方程组计算方法。该方法经n次迭代必收敛至理论上的精确解,且该方法对求解病态方程有效。 相似文献
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一、前言 在用势方程求解跨音流动的计算中,往往通过坐标变换将物理平面上的控制方程转换为计算平面上的控制方程进行求解。当采用非正交变换时,计算平面上的控制方程将产生交叉导数项。经离散化后差分方程中就含有相邻九个网格点上的参数。[1]的SIP方法不能同时求解与交叉导数项有关的参数,而是将其处理成求解方程的右端项,所求解的是五对角系数阵的线性代数方程组。对于强弯叶片和安装角较大的叶栅流场,交叉导数将产生重要影响,对此,本文提出一种SIP方法,能够直接求解九对角系数阵的线性代数方程组。 相似文献
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构造一类求解三种类型偏微分方程的间断Petrov-Galerkin方法.求解的方程分别含有二阶、三阶和四阶偏导数,包括Burgers型方程、KdV型方程和双调和型方程.首先将高阶微分方程转化成为与之等价的一阶微分方程组,再将求解双曲守恒律的间断Petrov-Galerkin方法用于求解微分方程组.该方法具有四阶精度且具有间断Petrov-Galerkin方法的优点.数值实验表明该方法可以达到最优收敛阶而且可以模拟复杂波形相互作用,如孤立子的传播及相互碰撞等. 相似文献
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构造一类求解三种类型偏微分方程的间断Petrov-Galerkin方法.求解的方程分别含有二阶、三阶和四阶偏导数,包括Burgers型方程、KdV型方程和双调和型方程.首先将高阶微分方程转化成为与之等价的一阶微分方程组,再将求解双曲守恒律的间断Petrov-Galerkin方法用于求解微分方程组.该方法具有四阶精度且具有间断Petrov-Galerkin方法的优点.数值实验表明该方法可以达到最优收敛阶而且可以模拟复杂波形相互作用,如孤立子的传播及相互碰撞等. 相似文献
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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
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In this article, we study the (2+1)-extension of Burgers equation and the KP equation. At first, based on a known Bäcklund transformation and corresponding Lax pair, an invariance which depends on two arbitrary functions
for (2+1)-extension of Burgers equation is worked out. Given a known solution and using the invariance, we can find solutions of the (2+1)-extension of Burgers equation repeatedly. Secondly, we put forward an invariance of Burgers equation which cannot be directly obtained by constraining the invariance of the (2+1)-extension of Burgers equation. Furthermore, we reveal that the invariance for finding the solutions of Burgers equation can
help us find the solutions of KP equation. At last, based on the
invariance of Burgers equation, the corresponding recursion
formulae for finding solutions of KP equation are digged out. As
the application of our theory, some examples have been put forward in this
article and some solutions of the (2+1)-extension of Burgers
equation, Burgers equation and KP equation are obtained. 相似文献
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In this paper, we present the local discontinuous Galerkin method for solving Burgers’ equation and the modified Burgers’ equation. We describe the algorithm formulation and practical implementation of the local discontinuous Galerkin method in detail. The method is applied to the solution of the one-dimensional viscous Burgers’ equation and two forms of the modified Burgers’ equation. The numerical results indicate that the method is very accurate and efficient. 相似文献
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THE EXACT SOLUTIONS OF THE BURGERS EQUATION AND HIGHER-ORDER BURGERS EQUATION IN (2+1) DIMENSIONS 下载免费PDF全文
Some exact solutions of the Burgers equation and higher-order Burgers equation in (2+1) dimensions are obtained by using the extended homogeneous balance method. In these solutions there are solitary wave solutions, close formal solutions for the initial value problems of the Burgers equation and higher-order Burgers equation, and also infinitely many rational function solutions. All of the solutions contain some arbitrary functions that may be related to the symmetry properties of the Burgers equation and the higher-order Burgers equation in (2+1) dimensions. 相似文献
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In this paper, a novel method, named the consistent Burgers equation expansion (CBEE) method, is proposed to solve nonlinear evolution equations (NLEEs) by the celebrated Burgers equation. NLEEs are said to be CBEE solvable if they are satisfied by the CBEE method. In order to verify the effectiveness of the CBEE method, we take (2+1)-dimensional Burgers equation as an example. From the (1+1)-dimensional Burgers equation, many new explicit solutions of the (2+1)-dimensional Burgers equation are derived. The obtained results illustrate that this method can be effectively extended to other NLEEs. 相似文献
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Burgers equation is reduced into a first-order ordinary differential equation by using travelling wave transformation and it has typical bifurcation characteristics.We can obtain many exact solutions of the Burgers equation,discuss its transcritical bifurcation and control dynamical behaviours by extending the stable region.The transcritical bifurcation exists in the (2 + 1)-dimensional Burgers equation. 相似文献
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《中国物理快报》2017,(3)
Nonlinear features of electron-acoustic shock waves are studied.The Burgers equation is derived and converted to the time fractional Burgers equation by Agrawal's method.Using the Adomian decomposition method,the shock wave solutions of the time fractional Burgers equation are constructed.The effect of time fractional parameter on the shock wave properties in auroral plasma is investigated. 相似文献
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H. G. Abdelwahed E. K. El-Shewy A. A. Mahmoud 《Journal of Experimental and Theoretical Physics》2016,122(6):1111-1116
The nonlinear properties of ion acoustic shock waves are studied. The Burgers equation is derived and converted into the time fractional Burgers equation by Agrawal’s method. Using the Adomian decomposition method, shock wave solutions of the time fractional Burgers equation are constructed. The effect of the time fractional parameter on the shock wave properties in ion-pair plasma is investigated. The results obtained may be important in investigating the broadband electrostatic shock noise in D- and F-regions of Earth’s ionosphere. 相似文献
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《Physics letters. A》2001,291(6):376-380
Making use of a extended tanh method with symbolic computation, we find a new complex line soliton for the two-dimensional (2D) KdV–Burgers equation. Its real part is the sum of the shock wave solution of a 2D Burgers equation and the solitary wave solution of a 2D KdV (KP) equation, and its imaginary part is the product of the shock wave solution of a 2D Burgers equation and the solitary wave solution of a 2D MKdV (MKP) equation. 相似文献
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In this paper, starting from the careful analysis on the characteristics of the Burgers equation and the KdV equation as well
as the KdV-Burgers equation, the superposition method is put forward for constructing the solitary wave solutions of the KdV-Burgers
equation from those of the Burgers equation and the KdV equation. The solitary wave solutions for the KdV-Burgers equation
are presented successfully by means of this method. 相似文献
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Generation of Nonlinear Evolution Equations by Reductions of the Self-Dual Yang–Mills Equations 总被引:1,自引:0,他引:1
With the help of some reductions of the self-dual Yang Mills (briefly written as sdYM) equations, we introduce a Lax pair whose compatibility condition leads to a set of (2 + 1)-dimensional equations. Its first reduction gives rise to a generalized variable-coefficient Burgers equation with a forced term. Furthermore, the Burgers equation again reduces to a forced Burgers equation with constant coefficients, the standard Burgers equation, the heat equation, the Fisher equation, and the Huxley equation, respectively. The second reduction generates a few new (2 + 1)-dimensional nonlinear integrable systems, in particular, obtains a kind of (2 + 1)-dimensional integrable couplings of a new (2 + 1)- dimensional integrable nonlinear equation. 相似文献