排序方式: 共有180条查询结果,搜索用时 140 毫秒
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陈至达 《应用数学和力学(英文版)》1984,5(5):1581-1585
Various exprressions of three-dimensional J integral are proposed. We derive here three-dimensional J integral by means of general potential energy principle and Green's theomem. Its physical meaning and application are shown in the paper, the results are true both for infinitesimal and finite deformation. 相似文献
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空间-时间分数阶对流扩散方程的数值解法 总被引:1,自引:0,他引:1
本文考虑一个空间-时间分数阶对流扩散方程.这个方程是将一般的对流扩散方程中的时间一阶导数用α(0<α<1)阶导数代替,空间二阶导数用β(1<β<2)阶导数代替.本文提出了一个隐式差分格式,验证了这个格式是无条件稳定的,并证明了它的收敛性,其收敛阶为O(ι h).最后给出了数值例子. 相似文献
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This paper studies synchronization of all nodes in a fractional-order complex dynamic network. An adaptive control strategy for synchronizing a dynamic network is proposed. Based on the Lyapunov stability theory, this paper shows that tracking errors of all nodes in a fractional-order complex network converge to zero. This simple yet practical scheme can be used in many networks such as small-world networks and scale-free networks. Unlike the existing methods which assume the coupling configuration among the nodes of the network with diffusivity, symmetry, balance, or irreducibility, in this case, these assumptions are unnecessary, and the proposed adaptive strategy is more feasible. Two examples are presented to illustrate effectiveness of the proposed method. 相似文献
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Ravi P. Agarwal Fatemah Mofarreh Rasool Shah Waewta Luangboon Kamsing Nonlaopon 《Entropy (Basel, Switzerland)》2021,23(8)
This research article is dedicated to solving fractional-order parabolic equations using an innovative analytical technique. The Adomian decomposition method is well supported by natural transform to establish closed form solutions for targeted problems. The procedure is simple, attractive and is preferred over other methods because it provides a closed form solution for the given problems. The solution graphs are plotted for both integer and fractional-order, which shows that the obtained results are in good contact with the exact solution of the problems. It is also observed that the solution of fractional-order problems are convergent to the solution of integer-order problem. In conclusion, the current technique is an accurate and straightforward approximate method that can be applied to solve other fractional-order partial differential equations. 相似文献
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The high-order implicit finite difference schemes for solving the fractionalorder Stokes’ first problem for a heated generalized second grade fluid with the Dirichlet boundary condition and the initial condition are given. The stability, solvability, and convergence of the numerical scheme are discussed via the Fourier analysis and the matrix analysis methods. An improved implicit scheme is also obtained. Finally, two numerical examples are given to demonstrate the effectiveness of the mentioned schemes. 相似文献
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Yan-Mei Lu 《中国物理 B》2022,31(6):60502-060502
The exploration of the memristor model in the discrete domain is a fascinating hotspot. The electromagnetic induction on neurons has also begun to be simulated by some discrete memristors. However, most of the current investigations are based on the integer-order discrete memristor, and there are relatively few studies on the form of fractional order. In this paper, a new fractional-order discrete memristor model with prominent nonlinearity is constructed based on the Caputo fractional-order difference operator. Furthermore, the dynamical behaviors of the Rulkov neuron under electromagnetic radiation are simulated by introducing the proposed discrete memristor. The integer-order and fractional-order peculiarities of the system are analyzed through the bifurcation graph, the Lyapunov exponential spectrum, and the iterative graph. The results demonstrate that the fractional-order system has more abundant dynamics than the integer one, such as hyper-chaos, multi-stable and transient chaos. In addition, the complexity of the system in the fractional form is evaluated by the means of the spectral entropy complexity algorithm and consequences show that it is affected by the order of the fractional system. The feature of fractional difference lays the foundation for further research and application of the discrete memristor and the neuron map in the future. 相似文献
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