共查询到20条相似文献,搜索用时 125 毫秒
1.
《数学物理学报(A辑)》2010,(1)
该文对求解非线性耦合Schrdinger方程的Sonnier-Christov格式进行了数值分析,证明了格式关于L_2范数的稳定性和二阶收敛性,运用Brouwer不动点定理证明了差分解的存在唯一性,给出一个求解非线性差分方程组的迭代算法并证明了算法的收敛性,最后对双孤立波的碰撞进行了模拟. 相似文献
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本文对一类非线性Sine-Gordon方程的初边值问题提出了两个隐式差分格式.两个隐式差分格式的精度均为O(τ~2 h~2).我们用离散泛函分析的方法证明了格式的收敛性和稳定性,并证明了求解格式的追赶迭代法的收敛性,最后给出了数值结果.结果表明本文的格式是有效的和可靠的. 相似文献
3.
本文提出求解两相渗流问题的一类克服数值弥散的特征混合元方法,用混合元法求解压力方程,利用后退特征线方法导出饱和度沿流线的移动;证明了格式的L∞稳定性和收敛性,并给出最优阶的误差估计。 相似文献
4.
针对研究吊桥模型而建立的四阶微积分方程, 提出Legendre谱逼近法进行求解.构造迭代算法来求解得到的线性系统, 证明了迭代格式的收敛性, 对问题进行了误差分析.数值算例验证了迭代的收敛性和方法的高精度. 相似文献
5.
研究带有P0函数的非线性互补问题. 基于一个新的光滑函数, 把问题近似成参数化的光滑方程组, 并且给出一个新的非内点连续算法. 所给算法在每步迭代只需要求解一个线性方程组和执行一次Armijo类型的线搜索. 在不需要严格互补条件的情况下, 证明了算法是全局收敛和超线性收敛的. 并且, 在一个较弱的条件下该算法具有局部二阶收敛性. 数值实验证实了算法的可行性和有效性. 相似文献
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7.
谢亚君 《数学物理学报(A辑)》2021,(4):1066-1078
基于Halley方法及经典的牛顿法,通过引入适当参数和线搜索技术,该文提出了求解非线性方程组的一类新的牛顿型算法,并给出两种具体修正迭代格式.在适当假设下,证明了新算法的全局收敛性.数值实验结果表明该方法是可行有效的. 相似文献
8.
提出了求解非线性互补问题的一个逐次逼近拟牛顿算法。在适当的假设下,证明了该算法的全局收敛性和局部超线性收敛性。 相似文献
9.
本文提出了一种求解等式约束非线性规划的新方法-线性代数方程组求解方法。我们证明了该算法具有全局收敛性和局部二阶收敛性。 相似文献
10.
本文构造了求解无约束非线性lp问题的新方法——调节熵函数法。给出了数值算法,证明了算法的收敛性。通过数值仿真将该方法与求解无约束非线性lp问题的极大熵函数法进行了比较,表明该算法是十分有效的。 相似文献
11.
《Journal of Computational and Applied Mathematics》1998,98(2):289-304
In this paper, we have proved the second-order convergence in L∞ norm of the Tsertsvadze's difference scheme for the Kuramoto-Tsuzuki equation. The existence, uniqueness and iterative algorithm are also discussed in detail. Furthermore, a L∞ second order convergent linearized difference scheme is given for inhomogeneous equation. All results are obtained without any restrictions on the meshsizes. At last a numerical example is presented. 相似文献
12.
In this article, a Crank‐Nicolson‐type finite difference scheme for the two‐dimensional Burgers' system is presented. The existence of the difference solution is shown by Brouwer fixed‐point theorem. The uniqueness of the difference solution and the stability and L2 convergence of the difference scheme are proved by energy method. An iterative algorithm for the difference scheme is given in detail. Furthermore, a linear predictor–corrector method is presented. The numerical results show that the predictor–corrector method is also convergent with the convergence order of two in both time and space. At last, some comments are provided for the backward Euler scheme. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 相似文献
13.
提出了一个基于三角形网格的显式差分格式逼近带有不连续系数的线性输运方程. 通过对数值解的有界性、TVD(total variation decreasing)和空间、时间方向的平移估计, 利用Kolmogorov紧性原理证明了数值解在L1loc模下收敛于初值问题的唯一弱解.从而得到了初值问题解的存在唯一性和关于初值的稳定性. 数值算例表明本文提出的格式计算方便而且比 Lax-Friedrichs格式更有效.
相似文献
14.
In this paper, we propose a robust semi-explicit difference scheme for solving the Kuramoto–Tsuzuki equation with homogeneous boundary conditions. Because the prior estimate in L∞-norm of the numerical solutions is very hard to obtain directly, the proofs of convergence and stability are difficult for the difference scheme. In this paper, we first prove the second-order convergence in L2-norm of the difference scheme by an induction argument, then obtain the estimate in L∞-norm of the numerical solutions. Furthermore, based on the estimate in L∞-norm, we prove that the scheme is also convergent with second order in L∞-norm. Numerical examples verify the correction of the theoretical analysis. 相似文献
15.
This paper presents a new difference scheme for numerical solution of stiff systems of ODE’s. The present study is mainly motivated to develop an absolutely stable numerical method with a high order of approximation. In this work a double implicit A-stable difference scheme with the sixth order of approximation is suggested. Another purpose of this study is to introduce automatic choice of the integration step size of the difference scheme which is derived from the proposed scheme and the one step scheme of the fourth order of approximation. The algorithm was tested by means of solving the Kreiss problem and a chemical kinetics problem. The behavior of the gas explosive mixture (H 2 + O2) in a closed space with a mobile piston is considered in test problem 2. It is our conclusion that a hydrogen-operated engine will permit to decrease the emitted levels of hazardous atmospheric pollutants. 相似文献
16.
Ling‐yun Zhang Zhi‐zhong Sun 《Numerical Methods for Partial Differential Equations》2004,20(2):230-247
A linearized three‐level difference scheme on nonuniform meshes is derived by the method of the reduction of order for the Neumann boundary value problem of a nonlinear parabolic system. It is proved that the difference scheme is uniquely solvable and second‐order convergent in L∞‐norm. A numerical example is given. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 230–247, 2004 相似文献
17.
Hai‐Yan Cao Zhi‐Zhong Sun Guang‐Hua Gao 《Numerical Methods for Partial Differential Equations》2014,30(2):451-471
The Camassa–Holm (CH) system is a strong nonlinear third‐order evolution equation. So far, the numerical methods for solving this problem are only a few. This article deals with the finite difference solution to the CH equation. A three‐level linearized finite difference scheme is derived. The scheme is proved to be conservative, uniquely solvable, and conditionally second‐order convergent in both time and space in the discrete L∞ norm. Several numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 451–471, 2014 相似文献
18.
This article is concerned with a high‐order difference scheme presented by Jain, Jain, and Mohanty for the nonlinear parabolic equation uxx = F(x, t, u, ut, ux) with Dirichlet boundary conditions. The solvability of the difference scheme is proved by Brower's fixed point theorem and the uniqueness of the difference solution is obtained by showing that the coefficient matrix is strictly column‐wise diagonal dominant. The boundedness and convergence of the difference scheme are obtained. The convergence order is 4 in space and 2 in time in L∞‐norm. A numerical example is provided to illustrate the validity of the theoretical results. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq , 2006 相似文献
19.
We study the long-time behavior of the finite difference solution to the generalized Kuramoto-Sivashinsky equation in two space dimensions with periodic boundary conditions. The unique solvability of numerical solution is shown. It is proved that there exists a global attractor of the discrete dynamical system and the upper semicontinuity d(Ah,τ,A)→0. Finally, we obtain the long-time stability and convergence of the difference scheme. Our results show that the difference scheme can effectively simulate the infinite dimensional dynamical systems. 相似文献
20.
Lih-Ing W. Roeger Roger W. Barnard 《Journal of Difference Equations and Applications》2013,19(4):333-340
We apply the central difference method (u t+1 ? u t ? 1)/(2Δt) = f(u t ) to an epidemic SIR model and show how the local stability of the equilibria is changed after applying the numerical method. The above central difference scheme can be used as a numerical method to produce a discrete-time model that possesses interesting local dynamics which appears inconsistent with the continuous model. Any fixed point of a differential equation will become an unstable saddle node after applying this method. Two other implicitly defined central difference methods are also discussed here. These two methods are more efficient for preserving the local stability of the fixed points for the continuous models. We apply conformal mapping theory in complex analysis to verify the local stability results. 相似文献