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1.
用三角级数和Maple软件求Burgers方程的精确解 总被引:2,自引:1,他引:1
用三角级数试探求解Burgers方程,得到关于待定系数的非线性代数方程组,利用Maple软件求解此非线性代数方程组,进而求得Burgers方程的精确解. 相似文献
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The structure of the stationary metrics [1], generated from Laplace’s solutions as seed, is investigated. The expressions
for the equatorial and polar circumferences, the surface area of the event horizon, location of singular points and the Gaussian
curvatures of the metrics [1] are derived and their variations with the field parameter α0 are studied. The multipole moments are calculated with the help of coordinate invariant Geroch-Hansen technique. These investigations
expose some interesting properties of the metrics, some of which are known in the literature and some deserve a new interpretation. 相似文献
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The structure of solutions of a stationary nonisothermal problem of the two-phase filtration of immiscible fluids is studied
numerically. The character of the convergence of nonstationary solutions to stationary ones is investigated. It is shown that
at different parameter values the solution may have an interval, where s(x) ≡ 0 or s(x) ≡ 1. The temperature effect on the structure of the solutions of the equation for water saturation is investigated.
The work was partially supported by the SB RAS (Integration Project No. 117). 相似文献
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An exact expression of the stationary distribution is found for a particular chemical model without detailed balance. An analytical approximation of this solution is obtained for small values of the concentration. It is shown that the WKB continuous approximation of the distribution is valid for all values of the concentration. 相似文献
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M. A. P. Martins 《General Relativity and Gravitation》1996,28(11):1309-1320
We study some known static vacuum solutions of Einstein's equations, namely, the A and B metrics of Ehlers and Kundt. All of them have axial symmetry, so they can be transformed to the Weyl form. In Weyl coordinates log –g
44 obeys a Laplace equation, and from this a source, calledthe Newtonian image source, can be identified. We use the image sources to give a possible interpretation to the metrics. The procedure is successful in some cases. In others it fails because the Weyl transform does not have reasonable properties at infinity. 相似文献
8.
From the point of view of approximate symmetry, the modified
Korteweg--de Vries--Burgers (mKdV--Burgers) equation with weak
dissipation is investigated. The symmetry of a system of the
corresponding partial differential equations which approximate the
perturbed mKdV--Burgers equation is constructed and the
corresponding general approximate symmetry reduction is derived;
thereby infinite series solutions and general formulae can be
obtained. The obtained result shows that the zero-order similarity
solution to the mKdV--Burgers equation satisfies the Painlevé II
equation. Also, at the level of travelling wave reduction, the
general solution formulae are given for any travelling wave solution
of an unperturbed mKdV equation. As an illustrative example, when
the zero-order tanh profile solution is chosen as an initial
approximate solution, physically approximate similarity solutions
are obtained recursively under the appropriate choice of parameters
occurring during computation. 相似文献
9.
当薛定谔方程中出现高次非谐振子势,电偶极矩势,分子晶体势,极化等效势等高次正幂与逆幂势函数以及它们的叠加时,薛定谔方程的求解变得非常复杂,本文采用奇点邻域附近的级数解法与求解渐近解相结合并且通过系数比较法,得到势函数为V(r)=a1r6 a2r2 a3r-4 a4r-6的径向薛定谔方程的一系列定态波函数解析解以及能级结构,并作了适当讨论与结论. 相似文献
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We consider the flow of a gas in a channel whose walls are kept at fixed (different) temperatures. There is a constant external force parallel to the boundaries which may themselves also be moving. The system is described by the stationary Boltzmann equation to which are added Maxwellian boundary conditions with unit accommodation coefficient. We prove that when the temperature gap, the relative velocity of the planes, and the force are all sufficiently small, there is a solution which converges, in the hydrodynamic limit, to a local Maxwellian with parameters given by the stationary solution of the corresponding compressible Navier-Stokes equations with no-slip voundary conditions. Corrections to this Maxwellian are obtained in powers of the Knudsen number with a controlled remainder. 相似文献
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In this paper we extend recent results on the hydrodynamic Navier-Stokes limit of the stationary Boltzmann equation for the flow of a gas of hard spheres in a channel in the presence of an external force to the case of a hard intermolecular potential with Grad angular cutoff. We prove the convergence of the solution, for small Knudsen numbers, to the Maxwellian with parameters solving the corresponding Navier-Stokes equation. In the present case we only get polynomial decay of the solution for large velocities, instead of the exponential decay which holds for hard spheres. 相似文献
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F. Kowsary K. Pooladvand A. Pourshaghaghy 《Journal of Quantitative Spectroscopy & Radiative Transfer》2007,108(2):277-294
In this paper, an appropriate distribution of the heating elements’ strengths in a radiation furnace is estimated using inverse methods so that a pre-specified temperature and heat flux distribution is attained on the design surface. Minimization of the sum of the squares of the error function is performed using the variable metric method (VMM), and the results are compared with those obtained by the conjugate gradient method (CGM) established previously in the literature. It is shown via test cases and a well-founded validation procedure that the VMM, when using a “regularized” estimator, is more accurate and is able to reach at a higher quality final solution as compared to the CGM. The test cases used in this study were two-dimensional furnaces filled with an absorbing, emitting, and scattering gas. 相似文献
14.
Asymptotic solution of a weak nonlinear model for the mid-latitude stationary wind field of a two-layer barotropic ocean 下载免费PDF全文
A weak nonlinear model of a two-layer barotropic ocean with Rayleigh dissipation is built.The analytic asymptotic solution is derived in the mid-latitude stationary wind field,and the physical meaning of the corresponding problem is discussed. 相似文献
15.
非线性系统受迫振动的周期解 总被引:1,自引:1,他引:0
理论上采用近似法求解,并用数学软件作图,分析和讨论了单摆自由振动的非等时性以及非线性受迫振动周期解与线性受迫振动稳态解的重要差别. 相似文献
16.
A class of oscillator of the EI Nifio-Southern oscillation model is considered. Using Mawhin's continuation theorem, a result on the existence of periodic solutions for ENSO model is obtained. 相似文献
17.
Free vibration analysis of truncated conical shells with general elastic boundary conditions is presented in this paper. An accurate modified Fourier series solution is developed, in which, regardless of the boundary conditions, each displacement of the conical shell is invariantly expressed as a new form of improved series expansions composed of a standard Fourier series and closed-form auxiliary functions introduced to ensure and accelerate the convergence of the series expansion. All the expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh–Ritz method. By using the present method, conical shells with arbitrary boundary conditions including all classical and elastic end restraints can be solved in a unified form. The accuracy and convergence of the current approach are validated by numerical examples and comparison with FEM results and those from the literature, and excellent accuracy is demonstrated. Comprehensive studies on the effects of elastic restraint parameters, semi-vertex angle and the ratio of length to radius are also reported. Some new results are presented for cases with elastic boundary restraints which may serve as benchmark solution for future researches. 相似文献
18.
Douglas Poland 《Journal of statistical physics》1989,55(1-2):389-415
Exact 15-term series expansions are given for the cooperative kinetics of adsorption of particles to a one-dimensional lattice with nearest-neighbor exclusion. Padé approximants to various forms of the series accurately describe the relaxation process, which is found to be well-approximated by assuming instantaneous internal equilibrium on the lattice. The series do not describe the very last stages of decay to equilibrium well and it has not been possible to extract from them the limiting relaxation parameters. The series show that the rate of change of the particle density on the lattice is not analytic in the density when expanded about the equilibrium state. 相似文献
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对一个追线问题进行了讨论,指出了用解析法求解的局限性和数值解法的优点;并将问题推广到了一般情况,得到了有意义的结果. 相似文献