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71.
Jingtang Ma 《Journal of Computational and Applied Mathematics》2009,231(2):807-814
In this paper a class of weakly singular Volterra integral equations with an infinite set of solutions is investigated. Among the set of solutions only one particular solution is smooth and all others are singular at the origin. The numerical solution of this class of equations has been a difficult topic to analyze and has received much previous investigation. The aim of this paper is to improve the convergence rates by a graded mesh method. The convergence rates are proved and a variety of numerical examples are provided to support the theoretical findings. 相似文献
72.
73.
New numerical techniques are presented for the solution of a two-dimensional anomalous sub-diffusion equation with time fractional derivative. In these methods, standard central difference approximation is used for the spatial discretization, and, for the time stepping, two new alternating direction implicit (ADI) schemes based on the L1 approximation and backward Euler method are considered. The two ADI schemes are constructed by adding two different small terms, which are different from standard ADI methods. The solvability, unconditional stability and H1 norm convergence are proved. Numerical results are presented to support our theoretical analysis and indicate the efficiency of both methods. 相似文献
74.
The design of multichannel optical filter is studied theoretically. New efficient two-step method based on combination of 6-th moment minimization and straightforward numerical minimization is developed. It is applied to find a fiber Bragg grating profile with minimal refractive index variation for 5 ÷ 32 channels. Obtained results are closer to the theoretical limit than previously reported. 相似文献
75.
提出了一种新的磨光函数,在分析它与已有磨光函数不同特性的基础上,研究了将它用于求解非线性P_0互补问题时,其磨光路径的存在性和连续性,进而设计了求解一类非线性P_0互补问题的非单调磨光算法.在适当的假设条件下,证明了该算法的全局收敛性和局部超线性收敛性.数值算例验证了算法的有效性. 相似文献
76.
In this paper, we propose and analyze a spectral Jacobi-collocation method for the numerical solution of general linear fractional integro-differential equations. The fractional derivatives are described in the Caputo sense. First, we use some function and variable transformations to change the equation into a Volterra integral equation defined on the standard interval [-1,1]. Then the Jacobi–Gauss points are used as collocation nodes and the Jacobi–Gauss quadrature formula is used to approximate the integral equation. Later, the convergence order of the proposed method is investigated in the infinity norm. Finally, some numerical results are given to demonstrate the effectiveness of the proposed method. 相似文献
77.
78.
We study a time dependent eddy current equation for the magnetic field H accompanied with a nonlinear boundary condition, which is a generalization of the classical Silver–Müller condition for a non-perfect conductor. More exactly, the relation between the normal components of electric (E) and magnetic (H ) fields obeys the following power law (linearized for small and large values) ν×E=ν×(|H×ν|α−1H×ν) for some α∈(0,1]. We design a linear fully discrete approximation scheme to solve this nonlinear problem. The convergence of the approximations to a weak solution is proved, error estimates describing the dependence of the error on discretization parameters are derived as well. The efficiency of the proposed method is supported by numerical experiments. 相似文献
79.
80.
《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