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本文将给出一种求解非线性方程组的单纯形算法—同伦算法,并证明其收敛性定理.作为其应用,还将讨论算法在求解一类非线性算子方程(尤其是非线性微分方程)中的情形. 相似文献
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非线性波方程准确孤立波解的符号计算 总被引:75,自引:0,他引:75
该文将机械化数学方法应用于偏微分方程领域,建立了构造一类非线性发展方程孤立波解的一种统一算法,并在计算机数学系统上加以实现,推导出了一批非线性发展方程的精确孤立波解.算法的基本原理是利用非线性发展方程孤立波解的局部性特点,将孤立波表示为双曲正切函数的多项式.从而将非线性发展方程(组)的求解问题转化为非线性代数方程组的求解问题.利用吴文俊消元法在计算机代数系统上求解非线性代数方程组,最终获得非线性发展方程(组)的准确孤立波解. 相似文献
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本文给出求解具有等式约束和不等式约束的非线性优化问题的一阶信息和二阶信息的两个微分方程系统,问题的局部最优解是这两个微分方程系统的渐近稳定的平衡点,给出了这两个微分方程系统的Euler离散迭代格式并证明了它们的收敛性定理,用龙格库塔法分别求解两个微分方程系统.我们构造了搜索方向由两个微分系统计算,步长采用Armijo线搜索的算法分别求解这个约束最优化问题,在局部Lipschitz条件下基于二阶信息的微分方程系统的迭代方法具有二阶的收敛速度。我们给出的数值结果表明龙格库塔的微分方程算法具有较好的稳定性和更高的精确度,求解二阶信息的微分方程系统的方法具有更快的收敛速度. 相似文献
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1.引言考虑非线性代数方程组这里, 为连续的对角映射,二者的导函数均存在,但并不一定连续.这类非线性代数方程组具有丰富的实际背景.譬如,Stefan问题和许多弱非线性椭圆型偏微分方程,就可归结为(1.1)的数值求解问题.根据方程组(1.1)的特殊结构,并利用矩阵多重分裂思想,文tZ]讨论了一类并行非线性Gauss-Seidel型迭代算法.这类算法具有很好的数值性质和较高的并行效率·在此基础上,运用松弛加速技术,文[8]进一步研究了一类并行多分… 相似文献
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首次利用三次样条配置方法采用直接法求解了一类非线性分数阶延迟微分方程初值问题,并给出了方法的局部截断误差和若干数值算例.数值结果表明方法求解分数阶延迟微分方程初值问题是非常有效的,结果对于未来研究分数阶延迟微分方程的数值方法具有重要的意义. 相似文献
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本文对静态非线性投入产出模型进行了一些理论探讨,证明了完全消耗系数的存在性并给出算法:提出并证明了新的一类非线性投入产出模型的求解条件;讨论了模型解的显著性区间. 相似文献
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In this paper the optimal control of uncertain parabolic systems of partial differential equations is investigated. In order to search for controllers that are insensitive to uncertainties in these systems, an iterative optimization procedure is proposed. This procedure involves the solution of a set of operator valued parabolic partial differential equations. The existence and uniqueness of solutions to these operator equations is proved, and a stable numerical algorithm to approximate the uncertain optimal control problem is proposed. The viability of the proposed algorithm is demonstrated by applying it to the control of parabolic systems having two different types of uncertainty. 相似文献
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Radial basis function method is an effective tool for solving differential equations in engineering and sciences. Many radial basis functions contain a shape parameter c which is directly connected to the accuracy of the method. Rippa [1] proposed an algorithm for selecting good value of shape parameter c in RBF-interpolation. Based on this idea, we extended the proposed algorithm for selecting a good value of shape parameter c in solving time-dependent partial differential equations. 相似文献
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An adaptive discretization algorithm for the weak approximation of stochastic differential equations
Andreas Rßler 《PAMM》2004,4(1):19-22
Numerical methods with fixed step size have limitations if they are applied for example to stiff stochastic differential equations where the step size is forced to be very small. In this paper, an adaptive step size control algorithm for the weak approximation of stochastic differential equations is introduced. The proposed algorithm calculates an estimation of the local error in order to determine the optimal step size such that the local error is bounded by some given tolerances. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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A new algorithm for calculating the two-dimensional differential transform of nonlinear functions is developed in this paper. This new technique is illustrated by studying suitable forms of nonlinearity. Three strongly nonlinear partial differential equations are then solved by differential transform method to demonstrate the validity and applicability of the proposed algorithm. The present framework offers a computationally easier approach to compute the transformed function for all forms of nonlinearity. This gives the technique much wider applicability. 相似文献
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In this paper, the problem of computing the suboptimal output feedback gains of decentralized control systems is investigated. First, the problem is formulated. Then, the gradient matrices based on the index function are derived and a new algorithm is established based on some nice properties. This algorithm shows that a suboptimal gain can be computed by solving several ordinary differential equations (ODEs). In order to find an initial condition for the ODEs, an algorithm for finding a stabilizing output feedback gain is exploited, and the convergence of this algorithm is discussed. Finally, an example is given to illustrate the proposed algorithm. 相似文献
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Manoj P. Tripathi Vipul K. Baranwal Ram K. Pandey Om P. Singh 《Communications in Nonlinear Science & Numerical Simulation》2013,18(6):1327-1340
In this paper, we propose a new numerical algorithm for solving linear and non linear fractional differential equations based on our newly constructed integer order and fractional order generalized hat functions operational matrices of integration. The linear and nonlinear fractional order differential equations are transformed into a system of algebraic equations by these matrices and these algebraic equations are solved through known computational methods. Further some numerical examples are given to illustrate and establish the accuracy and reliability of the proposed algorithm. The results obtained, using the scheme presented here, are in full agreement with the analytical solutions and numerical results presented elsewhere. 相似文献
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This paper presents a new method for validating existence and uniqueness of the solution of an initial value problems for fractional differential equations. An algorithm selecting a stepsize and computing a priori constant enclosure of the solution is proposed. Several illustrative examples, with linear and nonlinear fractional differential equations, are given to demonstrate the effectiveness of the method. 相似文献
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Hyunsoo Kim Rathinasamy Sakthivel 《Communications in Nonlinear Science & Numerical Simulation》2012,17(10):3788-3794
The hybrid fuzzy differential equations have a wide range of applications in science and engineering. This paper considers numerical solution for hybrid fuzzy differential equations. The improved predictor–corrector method is adapted and modified for solving the hybrid fuzzy differential equations. The proposed algorithm is illustrated by numerical examples and the results obtained using the scheme presented here agree well with the analytical solutions. The computer symbolic systems such as Maple and Mathematica allow us to perform complicated calculations of algorithm. 相似文献
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We propose an extrapolation algorithm for initial value problems in ordinary differential equations. In the algorithm, an appropriately chosen stepsizeH is divided into smaller stepsizes by a sequence and a new stopping rule is proposed. The sequences applied to the algorithm are Romberg {2,4,8,16,32,...}, Bulirsch {2,4,6,8,16...} and Harmonic {2,4,6,8,10,12,...} types. The proposed algorithm is compared numerically with the algorithm introduced by Stoer. In view of the accuracy of numerical solutions, the relatively small number of calculations, the stability and reliability of the algorithm, we found that the algorithm with the Romberg sequence is the best. 相似文献