共查询到20条相似文献,搜索用时 218 毫秒
1.
2.
3.
利用同伦分析法求解了(2+1)维改进的 Zakharov-Kuznetsov方程, 得到了它的近似周期解,该解与精确解符合很好. 结果表明,同伦分析法在求解高维非线性演化方程时, 仍然是一种行之有效的方法. 同时,还对该方法进行了一定的扩展, 经过扩展后的方法能够更方便地求解更多非线性演化方程的高精度近似解析解.
关键词:
同伦分析法
改进的 Zakharov-Kuznetsov方程
周期解 相似文献
4.
5.
6.
为了研究非线性发展方程的有界衰减振荡解,特选取Fisher方程为例. Fisher方程在描述激发介质的非数值模型(如Belousov-Zhabotinsky (BZ)反应)中, 其解的振幅取负值是有意义的.应用平面动力系统理论,研究了Fisher方程有界行波解存在的条件, 利用LS解法和线性化解法给出了其有界衰减振荡解的近似解析表达式,并进行了误差估计. 相似文献
7.
利用Excel作图和二分法结合解超越方程,既能总体上把握解的概况,又能快速地得到各个解的高精度近似结果,是一种简单、实用的超越方程解法。 相似文献
8.
9.
迎风紧致格式求解Hamilton-Jacobi方程 总被引:1,自引:1,他引:0
基于Hamilton-Jacobi(H-J)方程和双曲型守恒律之间的关系,将三阶和五阶迎风紧致格式推广应用于求解H-J方程,建立了高精度的H-J方程求解方法.给出了一维和二维典型数值算例的计算结果,其中包括一个平面激波作用下的Richtmyer Meshkov界面不稳定性问题.数值试验表明,在解的光滑区域该方法具有高精度,而在导数不连续的不光滑区域也获得了比较好的分辨效果.相比于同阶精度的WENO格式,本方法具有更小的数值耗散,从而有利于多尺度复杂流动的模拟中H-J方程的求解. 相似文献
10.
11.
Nonlinear elliptic partial differential equations are important to many large scale engineering and science problems. For this kind of equations, this article discusses a splitting extrapolation which possesses a high order of accuracy, a high degree of parallelism, less computational complexity and more flexibility than Richardson extrapolation. According to the problems, some domain decompositions are constructed and some independent mesh parameters are designed. Multi-parameter asymptotic expansions are proved for the errors of approximations. Based on the expansions, splitting extrapolation formulas are developed to compute approximations with high order of accuracy on a globally fine grid. Because these formulas only require us to solve a set of smaller discrete subproblems on different coarser grids in parallel instead of on the globally fine grid, a large scale multidimensional problem is turned into a set of smaller discrete subproblems. Additionally, this method is efficient for solving interface problems. 相似文献
12.
Asymptotic solution for a perturbed mechanism of western boundary undercurrents in the Pacific 总被引:1,自引:0,他引:1 下载免费PDF全文
This paper consider a class of perturbed mechanism for the western
boundary undercurrents in the Pacific. The model of generalized
governing equations is studied. Using the perturbation method, it
constructs the asymptotic solution of the model. And the accuracy of
asymptotic solution is proved by the theory of differential
inequalities. Thus the uniformly valid asymptotic expansions of the
solution are obtained. 相似文献
13.
14.
15.
The Newman-Penrose nonlinear asymptotic field equations are separated in terms of spin weight spherical harmonics (s.w.s.h.).
As an example, the results are used to study the radiation effects on a two-body system. The presence of radiation is manifest
through the nonlinear terms in the asymptotic equations. If these terms are assumed to be small, the asymptotic equations
can be formally solved by an iteration procedure. For the above example the first step of the iteration procedure is implemented
to an accuracy that includes the effects of radiation up to octopole order. The results illustrate the usual internal decay
of the orbit as well as an acceleration of the system's center of mass. In favorable cases, the two-body source can reach
significant velocities due to the radiation reaction. 相似文献
16.
The artificial compressibility method for the incompressible Navier–Stokes equations is revived as a high order accurate numerical method (fourth order in space and second order in time). Similar to the lattice Boltzmann method, the mesh spacing is linked to the Mach number. An accuracy higher than that of the lattice Boltzmann method is achieved by exploiting the asymptotic behavior of the solution of the artificial compressibility equations for small Mach numbers and the simple lattice structure. An easy method for accelerating the decay of acoustic waves, which deteriorate the quality of the numerical solution, and a simple cure for the checkerboard instability are proposed. The high performance of the scheme is demonstrated not only for the periodic boundary condition but also for the Dirichlet-type boundary condition. 相似文献
17.
The method of self-similar factor approximants is shown to be very convenient for solving different evolution equations and boundary-value problems typical of physical applications. The method is general and simple, being a straightforward two-step procedure. First, the solution to an equation is represented as an asymptotic series in powers of a variable. Second, the series are summed by means of the self-similar factor approximants. The obtained expressions provide highly accurate approximate solutions to the considered equations. In some cases, it is even possible to reconstruct exact solutions for the whole region of variables, starting from asymptotic series for small variables. This can become possible even when the solution is a transcendental function. The method is shown to be more simple and accurate than different variants of perturbation theory with respect to small parameters, being applicable even when these parameters are large. The generality and accuracy of the method are illustrated by a number of evolution equations as well as boundary value problems. 相似文献
18.
Felix Rieper 《Journal of computational physics》2011,230(13):5263-5287
We present a low-Mach number fix for Roe’s approximate Riemann solver (LMRoe). As the Mach number Ma tends to zero, solutions to the Euler equations converge to solutions of the incompressible equations. Yet, standard upwind schemes do not reproduce this convergence: the artificial viscosity grows like 1/Ma, leading to a loss of accuracy as Ma → 0. With a discrete asymptotic analysis of the Roe scheme we identify the responsible term: the jump in the normal velocity component ΔU of the Riemann problem. The remedy consists of reducing this term by one order of magnitude in terms of the Mach number. This is achieved by simply multiplying ΔU with the local Mach number. With an asymptotic analysis it is shown that all discrepancies between continuous and discrete asymptotics disappear, while, at the same time, checkerboard modes are suppressed. Low Mach number test cases show, first, that the accuracy of LMRoe is independent of the Mach number, second, that the solution converges to the incompressible limit for Ma → 0 on a fixed mesh and, finally, that the new scheme does not produce pressure checkerboard modes. High speed test cases demonstrate the fall back of the new scheme to the classical Roe scheme at moderate and high Mach numbers. 相似文献
19.
The expansion of a distribution function in spherical harmonics transforms the Boltzmann equation into a system of integro-differential
equations with kernels depending only of the magnitudes of velocities. The kernels can be expressed in terms of the sums including
the matrix elements (MEs) of the collision integral. The kernels are constructed using new results of ME calculations; analysis
of errors is carried out with the help of analytic expressions for kernels, which were derived by Hilbert and Hecke for the
hard-sphere model. The concept of generalized matrix elements is introduced and their asymptotic representation is constructed
for large values of indices. Analytic expressions for the contribution from MEs with large indices to the kernels are constructed.
The high accuracy of the construction of a kernel using MEs is demonstrated. 相似文献
20.
The generating functions for the collision brackets associated with two alternative convergent kinetic equations are derived for small values of the plasma parameter. It is shown that the first few terms in the asymptotic expansions of these generating functions are identical. Consequently, both kinetic equations give rise to the same transport coefficients in arbitrarily high order of the Chapman-Cowling truncation scheme. 相似文献