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1.
拟线性双曲型方程的A.D.I.Galerkin方法及其敛速估计   总被引:11,自引:0,他引:11  
王申林  孙淑英 《计算数学》1987,9(3):233-242
§1.引言 本文讨论求解一类二维拟线性双曲型方程的有限元方法([1,4,7]是本文的特殊情形),提出解该方程的 A.D.I.Galerkin方法,并给出最优 H~1模误差估计.[7]中导出了非线性方程组,而本文导出的是U_(ij)~(n+1)的线性方程组.交替方向格式将二维问题化成一维,其计算量比[1,4,7]中诸格式小得多;又在估计误差时,用本文的方法得到的估计式不  相似文献   

2.
陈志红  李东升 《数学学报》2019,62(3):381-390
本文研究了R~3中有界区域Ω上的电磁场方程组弱解的W~(1,p)估计.该方程组来自于磁场所满足的稳态麦克斯韦方程组.在假定系数矩阵的逆属于VMO空间的条件下,利用R~3中向量场的旋度和散度的性质,将该方程组转化为标量椭圆型方程组,从而根据椭圆型方程组的正则性理论,得到解的W~(1,p)估计,其中1

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3.
根据Hopf-Cole变换法和试探函数法的基本思想,引入一个变换,并把它应用于求解(2+1)维破裂孤子方程组、(2+1)维Nizhnik-Novikov-Vesslov方程组和(2+1)维Broer-Kaup方程组,得到了这三个方程组的许多新的解析解,包括孤波解和奇异行波解.该方法也适用于其它方程组.  相似文献   

4.
本文考虑连串反应中控制火焰的耦合广义Kuramoto Sivashinsky-Ginzburg Landau(GKS-CGL)方程组的周期初值问题,主要研究其解在系数g→0和δ→0时的极限行为.首先,采用Galerkin方法,通过构造一系列精细的先验估计,得到GKS-CGL方程组周期初值问题整体光滑解的存在唯一性.其次,利用一致有界估计证得GKS-CGL方程组极限解收敛,并给出解的收敛率估计.  相似文献   

5.
本文构造了计算二维可压缩流动的差分格式,严格估计了周期解问题的误差,并由此得到其收敛性.文中还严格估计了某一类初-边值问题的误差,并得到相应的收敛性.本文方法可推广应用于电磁流体力学方程组等.  相似文献   

6.
本文讨论了具弱衰减Cauchy初值的不同速度半线性Klein-Gordon方程组解的生命区间估计问题.当初值具有尺度∈时,得到生命区间的下界估计∈-2|log ∈|-α(当空间维数d≥3时α=2,当d=2时α=3).  相似文献   

7.
一类非牛顿渗流系统爆破界的估计   总被引:4,自引:1,他引:3  
首先得到一类拟线性椭圆型方程组的正解的先验界估计和衰减性质,从而推出该方程组的径向非增正对称解的不存在性结果.利用此结果建立了一类拟线性反应扩散方程组(非牛顿渗流系统)的爆破界的估计,推广了半线性(Fujita型)反应扩散方程组的结果.  相似文献   

8.
余王辉 《数学年刊A辑》2001,22(5):535-548
本文证明了当Ginzburg-Landau参数足够大时,一维Ginzburg-Landau超导方程组的对称解是唯一的.该问题的难点在于所考虑的解具有“奇点”也即,当Ginzburg-Landau参数趋于无穷大时,解的导数在这些点处趋于无穷.证明的关键是要得到解在这些奇点近旁的精细估计.  相似文献   

9.
本文讨论了具弱衰减Cauchy初值的不同速度半线性Klein-Gordon方程组解的生命区间估计问题.当初值具有尺度ε时,得到生命区间的下界估计ε-2|logε|-α。(当空间维数d≥3时。α=2,当d=2时α=3).  相似文献   

10.
以浅水长波近似方程组为例,提出了拟小波方法求解(1 1)维非线性偏微分方程组数值解,该方程用拟小波离散格式离散空间导数,得到关于时间的常微分方程组,用四阶Runge-K utta方法离散时间导数,并将其拟小波解与解析解进行比较和验证.  相似文献   

11.
The velocity field corresponding to the Rayleigh–Stokes problem for an edge, in an incompressible generalized Oldroyd-B fluid has been established by means of the double Fourier sine and Laplace transforms. The fractional calculus approach is used in the constitutive relationship of the fluid model. The obtained solution, written in terms of the generalized G-functions, is presented as a sum of the Newtonian solution and the corresponding non-Newtonian contribution. The solution for generalized Maxwell fluids, as well as those for ordinary Maxwell and Oldroyd-B fluids, performing the same motion, is obtained as a limiting case of the present solution. This solution can be also specialized to give the similar solution for generalized second grade fluids. However, for simplicity, a new and simpler exact solution is established for these fluids. For β → 1, this last solution reduces to a previous solution obtained by a different technique.   相似文献   

12.
The velocity field corresponding to the Rayleigh–Stokes problem for an edge, in an incompressible generalized Oldroyd-B fluid has been established by means of the double Fourier sine and Laplace transforms. The fractional calculus approach is used in the constitutive relationship of the fluid model. The obtained solution, written in terms of the generalized G-functions, is presented as a sum of the Newtonian solution and the corresponding non-Newtonian contribution. The solution for generalized Maxwell fluids, as well as those for ordinary Maxwell and Oldroyd-B fluids, performing the same motion, is obtained as a limiting case of the present solution. This solution can be also specialized to give the similar solution for generalized second grade fluids. However, for simplicity, a new and simpler exact solution is established for these fluids. For β → 1, this last solution reduces to a previous solution obtained by a different technique.  相似文献   

13.
The dynamics of a predator–prey model with impulsive state feedback control, which is described by an autonomous system with impulses, is studied. The sufficient conditions of existence and stability of semi-trivial solution and positive period-1 solution are obtained by using the Poincaré map and analogue of the Poincaré criterion. The qualitative analysis shows that the positive period-1 solution bifurcates from the semi-trivial solution through a fold bifurcation. The bifurcation diagrams of periodic solutions are obtained by using the Poincaré map, and it is shown that a chaotic solution is generated via a cascade of period-doubling bifurcations.  相似文献   

14.
This article concerns a competition model in the unstirred chemostat. The bifurcation solution from a double eigenvalue is obtained. We see that this bifurcation solution connects the positive solution from the semitrivial solution (θ a ,?0) with that from the other semitrivial solution (0,?θ b ). Moreover, the asymptotic stability of the positive solution corresponding to this bifurcation is derived under certain conditions. The method we used here is based on spectral analysis, comparison principle, bifurcation theory and Lyapunov–Schmidt procedure.  相似文献   

15.
The dynamical behavior of an SIR epidemic model with birth pulse and pulse vaccination is discussed by means of both theoretical and numerical ways. This paper investigates the existence and stability of the infection-free periodic solution and the epidemic periodic solution. By using the impulsive effects, a Poincaré map is obtained. The Poincaré map, center manifold theorem, and bifurcation theorem are used to discuss flip bifurcation and bifurcation of the epidemic periodic solution. Moreover, the numerical results show that the epidemic periodic solution (period-one) bifurcates from the infection-free periodic solution through a supercritical bifurcation, the period-two solution bifurcates from the epidemic periodic solution through flip bifurcation, and the chaotic solution generated via a cascade of period-doubling bifurcations, which are in good agreement with the theoretical analysis.  相似文献   

16.
The method of decaying residual solution is applied to obtain an approximate interior solution for the torsion of slender prismatic elastic bodies under different end conditions. The approximate solution is generally accurate up to terms that are exponentially small in the length-to-cross-sectional-width ratio. For stress end conditions, the result is identical to the classical Saint-Venant torsion solution. Similar types of simple solutions, not known previously, are obtained for different types of mixed end conditions. For displacement conditions at both ends, the corresponding Saint-Venant type result requires an accurate solution of a canonical problem for a semi-infinite prismatic body that is to be obtained once and for all. The solution of the canonical problem is elementary for a circular cross section. The approximate interior solution in that case is identical to the known exact interior solution.  相似文献   

17.
《Quaestiones Mathematicae》2013,36(3):349-379
Abstract

The properties of the limit cycle of a generalised van der Pol equation of the form ü + u = ε (1—u2n)u, where ε is small and n is any positive integer, are investigated by applying a time transformation perturbation method due to Burton. It is found that as n increases the amplitude of the limit cycle oscillation decreases and its period increases. The time transformation solution is compared with the solution derived using the method of multiple scales and with a numerical solution. It is found that, to first order in ε, the time transformation solution for the limit cycle agrees better with the numerical solution than the multiple scales solution. Both perturbation solutions give the same result for the period of the limit cycle to second order in ε. The accuracy of the time transformation solution decreases as n increases.  相似文献   

18.
A general solution of equations of equilibrium in linear elasticity is presented in cylindrical coordinates in terms of three harmonic functions describing an arbitrary displacement field. The structure of this solution is similar to the general solution given by Love (Kelvin’s solution) in spherical coordinates. Galerkin vector representation of our solution leads to an integral connecting the harmonic functions. The connections to Papkovich–Neuber and Muki’s general representations are also provided. Suitable choices of the harmonic functions in our new representation yield general solutions for axisymmetric deformations due to Love, Boussinesq and Michell. Some unbounded deformations induced by singular forces are tabulated in terms of the scalar harmonic functions to justify the simple nature of our representation. Exact solution of the half-space boundary value problem is also provided to demonstrate the power of our approach. The stress components computed via our solution are also listed (see the Appendix).  相似文献   

19.
The object of this article is to present the solution of a fractional generalization of the Schrödinger equation of quantum mechanics in one dimension. The method followed in deriving the solution is that of joint Laplace and Fourier transforms. The solution is obtained in a compact and computational form in terms of the H-function. A result given earlier by Debnath for the solution of a generalized Schrödinger equation is obtained in an explicit form in terms of the H-function, as a special case of our findings.  相似文献   

20.
When the Jacobian of a computed numerical solution of a polynomial system in Cn allows very small singular values, the solution could be isolated with a multiple multiplicity or may belong to a solution component with positive dimension. The algorithm constructed in this article intends to differentiate those cases by determining the dimension of the solution component M in which the solution lies. Of particular interest is the case when dim(M)=0, then the solution is of course isolated. While the proposed algorithm is experimental, it has been tested successfully on the class of problems with the solution in question belonging to a reduced component. Numerical results are provided to illustrate the accuracy of the algorithm.  相似文献   

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