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991.
通过构造合适函数变换的方法,建立n维抛物型方程第二初边值问题古典解的最大模估计,并由此得到该定解问题解的唯一性和稳定性. 相似文献
992.
《Communications in Nonlinear Science & Numerical Simulation》2014,19(3):442-447
This paper considers the impulsive functional differential equations with infinite delays or finite delays. Some new sufficient conditions are obtained to guarantee the global exponential stability by employing the improved Razumikhin technique and Lyapunov functions. The result extends and improves some recent works. Moreover, the obtained Razumikhin condition is very simple and effective to implement in real problems and it is helpful to investigate the stability of delayed neural networks and synchronization problems of chaotic systems under impulsive perturbation. Finally, a numerical example and its simulation is given to show the effectiveness of the obtained result in this paper. 相似文献
993.
《Communications in Nonlinear Science & Numerical Simulation》2014,19(10):3513-3522
For arbitrary systems of two linear second-order ordinary differential equations, the symmetry Lie algebra is described in terms of invariant theory, resulting in eleven non-equivalent symmetry types. The result is compared with the group classification approach recently obtained by different authors. 相似文献
994.
《Communications in Nonlinear Science & Numerical Simulation》2014,19(9):2958-2973
The traditional Newton method for solving nonlinear operator equations in Banach spaces is discussed within the context of the continuous Newton method. This setting makes it possible to interpret the Newton method as a discrete dynamical system and thereby to cast it in the framework of an adaptive step size control procedure. In so doing, our goal is to reduce the chaotic behavior of the original method without losing its quadratic convergence property close to the roots. The performance of the modified scheme is illustrated with various examples from algebraic and differential equations. 相似文献
995.
《Communications in Nonlinear Science & Numerical Simulation》2014,19(9):2974-2982
For some abstract classes of nonlinear non-autonomous systems with variable and state-dependent delays existence, non-existence and multiplicity of periodic solutions are discussed. To illustrate the efficiency of the method, we obtain some well-known results for applied systems as corollaries of our existence theorems. 相似文献
996.
《Communications in Nonlinear Science & Numerical Simulation》2014,19(7):2172-2180
This paper presents the vortical and self-similar solutions for 2D compressible Euler equations using the separation method. These solutions complement Makino’s solutions in radial symmetry without rotation. The rotational solutions provide new information that furthers our understanding of ocean vortices and reference examples for numerical methods. In addition, the corresponding blowup, time-periodic or global existence conditions are classified through an analysis of the new Emden equation. A conjecture regarding rotational solutions in 3D is also made. 相似文献
997.
研究了Kenichiro提出的轮换对称形式的丢番图方程,即方程ab bc ca=ya+b+c3的求解问题,利用素数整除的一些性质,证明了该方程仅有平凡解a=b=c以及非平凡解(a,b,c)=(k,k,4k),(k,4k,k),(4k,k,k)(k∈N),从而完全解决了这个方程. 相似文献
998.
《Communications in Nonlinear Science & Numerical Simulation》2014,19(11):3929-3937
The paper is devoted to the study of the dynamical behavior of the solutions of stochastic FitzHugh–Nagumo lattice equations, driven by fractional Brownian motions, with Hurst parameter greater than 1/2. Under some usual dissipativity conditions, the system considered here features different dynamics from the same one perturbed by Brownian motion. In our case, the random dynamical system has a unique random equilibrium, which constitutes a singleton sets random attractor. 相似文献
999.
Hua‐Huai Chern María‐Inés Fernández‐Camacho Hsien‐Kuei Hwang Conrado Martínez 《Random Structures and Algorithms》2014,44(1):67-108
An unusual and surprising expansion of the form as , is derived for the probability pn that two randomly chosen binary search trees are identical (in shape, hence in labels of all corresponding nodes). A quantity arising in the analysis of phylogenetic trees is also proved to have a similar asymptotic expansion. Our method of proof is new in the literature of discrete probability and the analysis of algorithms, and it is based on the logarithmic psi‐series expansions for nonlinear differential equations. Such an approach is very general and applicable to many other problems involving nonlinear differential equations; many examples are discussed in this article and several attractive phenomena are discovered.Copyright © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 44, 67–108, 2014 相似文献
1000.
《Journal of the Egyptian Mathematical Society》2014,22(3):511-516
In this article, we present a new numerical method to solve the integro-differential equations (IDEs). The proposed method uses the Legendre cardinal functions to express the approximate solution as a finite series. In our method the operational matrix of derivatives is used to reduce IDEs to a system of algebraic equations. To demonstrate the validity and applicability of the proposed method, we present some numerical examples. We compare the obtained numerical results from the proposed method with some other methods. The results show that the proposed algorithm is of high accuracy, more simple and effective. 相似文献