共查询到20条相似文献,搜索用时 15 毫秒
1.
D. V. Valovik Yu. G. Smirnov E. Yu. Smol’kin 《Computational Mathematics and Mathematical Physics》2013,53(7):973-983
The paper is concerned with propagation of surface TE waves in a circular nonhomogeneous two-layered dielectric waveguide filled with a Kerr nonlinear medium. The problem is reduced to the analysis of a nonlinear integral equation with a kernel in the form of a Green’s function. The existence of propagating TE waves is proved using the contraction mapping method. For the numerical solution of the problem, two methods are proposed: an iterative algorithm (whose convergence is proved) and a method based on solving an auxiliary Cauchy problem (the shooting method). The existence of roots of the dispersion equation (propagation constants of the waveguide) is proved. Conditions under which k waves can propagate are obtained, and regions of localization of the corresponding propagation constants are found. 相似文献
2.
解非线性方程的自动调节阻尼法 总被引:1,自引:0,他引:1
解非线性方程组的一般方法是将其线性化,形成各种形式的迭代程序进行数值近似计算.对于复杂强非线性问题,在迭代过程中往往不易收敛,甚至数值失稳而发散.不能满足工程要求.常规的牛顿法及改进的牛顿法均未彻底解决这一问题,因而使得复杂强非线性问题的数值模拟计算受到了限制.本文提出一种新的方法---自动调节阻尼法,是对带阻尼因子的牛顿法的进一步改进.引进阻尼因子向量,在迭代过程中,通过判断与调整,不断地自动调节阻尼因子向量,引用有效收敛系数与加速系数,改善对赋初值的要求,加速求解的迭代过程,保证了复杂强非线性方程求解的稳定性.采用这一新的方法,已成功地数值模拟了飞机中的一些复杂的传热问题,可进一步推广用于非线性流动、传热、结构动力响应等各种复杂强非线性的工程问题的数值模拟计算. 相似文献
3.
Mohammad Tafakkori-Bafghi Ghasem Barid Loghmani Mohammad Heydari Xiaoli Bai 《Mathematical Methods in the Applied Sciences》2020,43(3):1084-1111
In this paper, an effective numerical iterative method for solving nonlinear initial value problems (IVPs) is presented. The proposed iterative scheme, called the Jacobi-Picard iteration (JPI) method, is based on the Picard iteration technique, orthogonal shifted Jacobi polynomials, and shifted Jacobi-Gauss quadrature formula. In comparison with traditional methods, the JPI method uses an iterative formula for updating next step approximations and calculating integrals of the shifted Jacobi polynomials are performed via an exact relation. Also, a vector-matrix form of the JPI method is provided in details which reduce the CPU time. The performance of the presented method has been investigated by solving several nonlinear IVPs. Numerical results show the efficiency and the accuracy of the proposed iterative method. 相似文献
4.
Yuan-Ming Wang 《Applied Numerical Mathematics》2011,61(1):38-52
The purpose of this paper is to give a numerical treatment for a class of strongly nonlinear two-point boundary value problems. The problems are discretized by fourth-order Numerov's method, and a linear monotone iterative algorithm is presented to compute the solutions of the resulting discrete problems. All processes avoid constructing explicitly an inverse function as is often needed in the known treatments. Consequently, the full potential of Numerov's method for strongly nonlinear two-point boundary value problems is realized. Some applications and numerical results are given to demonstrate the high efficiency of the approach. 相似文献
5.
Implicit iterative method acquires good effect in solving linear ill-posed problems. We have ever applied the idea of implicit iterative method to solve nonlinear ill-posed problems, under the restriction that α is appropriate large, we proved the monotonicity of iterative error and obtained the convergence and stability of iterative sequence, numerical results show that the implicit iterative method for nonlinear ill-posed problems is efficient. In this paper, we analyze the convergence and stability of the corresponding nonlinear implicit iterative method when αk are determined by Hanke criterion. 相似文献
6.
F.Z. Geng 《Journal of Computational and Applied Mathematics》2012,236(7):1789-1794
In this paper, an algorithm is presented for solving second-order nonlinear multi-point boundary value problems (BVPs). The method is based on an iterative technique and the reproducing kernel method (RKM). Two numerical examples are provided to show the reliability and efficiency of the present method. 相似文献
7.
Alexander G. Ramm Alexandra B. Smirnova 《Numerical Functional Analysis & Optimization》2013,34(3-4):317-332
A two-step iterative process for the numerical solution of nonlinear problems is suggested. In order to avoid the ill-posed inversion of the Fréchet derivative operator, some regularization parameter is introduced. A convergence theorem is proved. The proposed method is illustrated by a numerical example in which a nonlinear inverse problem of gravimetry is considered. Based on the results of the numerical experiments practical recommendations for the choice of the regularization parameter are given. Some other iterative schemes are considered. 相似文献
8.
This paper considers identification problems of nonlinear functions fitting or nonlinear systems modelling. A gradient based iterative algorithm and a Newton iterative algorithm are presented to determine the parameters of a nonlinear system by using the negative gradient search method and Newton method. Furthermore, two model transformation based iterative methods are proposed in order to enhance computational efficiencies. By means of the model transformation, a simpler nonlinear model is achieved to simplify the computation. Finally, the proposed approaches are analyzed using a numerical example. 相似文献
9.
Alfred Carasso 《Journal of Mathematical Analysis and Applications》1977,59(1):169-209
We construct and analyze an algorithm for the numerical computation of Burgers' equation for preceding times, given an a priori bound for the solution and an approximation to the terminal data. The method is based on the “backward beam equation” coupled with an iterative procedure for the solution of the nonlinear problem via a sequence of linear problems. We also present the results of several numerical experiments. It turns out that the procedure converges “asymptotically,” i.e., in the same manner in which an asymptotic expansion converges. This phenomenon seems related to the “destruction of information,” at t = 0, which is typical in backwards dissipative equations. We derive a priori stability estimates for the analytic backwards problem, and we observe that in many numerical experiments, the distance backwards in time where significant accuracy can be attained is much larger than would be expected on the basis of such estimates. The method is useful for small solutions. Problems where steep gradients occur require considerably more precision in measurement. The algorithm is applicable to other semilinear problems. 相似文献
10.
Andrzej Granas Ronald B. Guenther John W. Lee 《Journal of Fixed Point Theory and Applications》2009,6(1):27-61
Fixed point continuation methods and shooting methods are combined to produce an effective numerical procedure for solving
boundary value problems for nonlinear ordinary differential equations. Typical numerical solution schemes involve an iteration
procedure. Continuation methods systematically generate good initial guesses and, when combined with a shooting method and
an appropriate update procedure, give systematic means for the numerical solution of nonlinear boundary value problems. This
paper concentrates on problems of Bernstein type, which arise naturally in the calculus of variations and in steady-state
heat conduction. 相似文献
11.
Optimization algorithms usually rely on the setting of parameters, such as barrier coefficients. We have developed a generic
meta-control procedure to optimize the behavior of given iterative optimization algorithms. In this procedure, an optimal
continuous control problem is defined to compute the parameters of an iterative algorithm as control variables to achieve
a desired behavior of the algorithm (e.g., convergence time, memory resources, and quality of solution). The procedure is
illustrated with an interior point algorithm to control barrier coefficients for constrained nonlinear optimization. Three
numerical examples are included to demonstrate the enhanced performance of this method.
This work was primarily done when Z. Zabinsky was visiting Clearsight Systems Inc. 相似文献
12.
Virginia Alarcón Sergio Amat Sonia Busquier David J. López 《Journal of Computational and Applied Mathematics》2008
In this paper, a modified Steffensen's type iterative scheme for the numerical solution of a system of nonlinear equations is studied. Two convergence theorems are presented. The numerical solution of boundary-value problems by the multiple shooting method using the proposed iterative scheme is analyzed. 相似文献
13.
本文提出一种求解非线性有限元方程的逐层校正迭代法.有关数值分析表明,当网格分划较细,网格分划参数h_j较小时,仅需一次简单的迭代和校正步骤就可满足数值计算的要求,使用该方法的计算复杂性是最佳阶的,即为O(N_j),其中N_j为最细网格层上离散结点变量的数目. 相似文献
14.
B. M. Podlevs’kyi 《Journal of Mathematical Sciences》2009,160(3):357-367
The iterative algorithm for determination of bilateral (alternating) approximations to the eigenvalues of nonlinear spectral
problems that uses a bilateral analog of the Newton method and a new efficient numerical procedure for calculation of the
Newton correction and its derivative is proposed.
Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 1, pp. 65–73, January–March, 2008. 相似文献
15.
In this paper, our aim is to study a numerical method for an ultraparabolic equation with nonlinear source function. Mathematically, the bibliography on initial–boundary value problems for ultraparabolic equations is not extensive although the problems have many applications related to option pricing, multi-parameter Brownian motion, population dynamics and so forth. In this work, we present the approximate solution by virtue of finite difference scheme and Fourier series. For the nonlinear case, we use an iterative scheme by linear approximation to get the approximate solution and obtain error estimates. A numerical example is given to justify the theoretical analysis. 相似文献
16.
Tomas Johansson Daniel Lesnic 《Numerical Methods for Partial Differential Equations》2007,23(5):998-1017
In this article, an iterative algorithm based on the Landweber‐Fridman method in combination with the boundary element method is developed for solving a Cauchy problem in linear hydrostatics Stokes flow of a slow viscous fluid. This is an iteration scheme where mixed well‐posed problems for the stationary generalized Stokes system and its adjoint are solved in an alternating way. A convergence proof of this procedure is included and an efficient stopping criterion is employed. The numerical results confirm that the iterative method produces a convergent and stable numerical solution. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007 相似文献
17.
George Baravdish Olof Svensson Freddie Åström 《Numerical Functional Analysis & Optimization》2013,34(2):147-168
In this study, we investigate the backward p(x)-parabolic equation as a new methodology to enhance images. We propose a novel iterative regularization procedure for the backward p(x)-parabolic equation based on the nonlinear Landweber method for inverse problems. The proposed scheme can also be extended to the family of iterative regularization methods involving the nonlinear Landweber method. We also investigate the connection between the variable exponent p(x) in the proposed energy functional and the diffusivity function in the corresponding Euler-Lagrange equation. It is well known that the forward problems converges to a constant solution destroying the image. The purpose of the approach of the backward problems is twofold. First, solving the backward problem by a sequence of forward problems, we obtain a smooth image which is denoised. Second, by choosing the initial data properly, we try to reduce the blurriness of the image. The numerical results for denoising appear to give improvement over standard methods as shown by preliminary results. 相似文献
18.
一类椭圆型变分不等式离散问题的迭代算法 总被引:9,自引:1,他引:9
根据一类椭圆型变分不等式离散问题所具有的非线性特征,提出了一种简明快速的迭代算法,该方法在解决障碍问题及流体润滑油膜破裂自然边值问题等工程应用问题时具有较高的效率。 相似文献
19.
R. B. Kellogg 《Milan Journal of Mathematics》1990,60(1):167-176
Some iterative methods are considered for the numerical solution of convection diffusion problems. The first class of iterative methods is Chebyshev accelerated iterations. The issues of parameter selection and convergence rates are considered. Secondly, we consider convection—diffusion type iterations where the iterations are of Peaceman-Rachford type. Here, a conjecture is given concerning a related problem in functional analysis. Finally, we consider flow-directed iterative schemes. We describe some schemes of this class for an upwind difference method, and also for a nonlinear hyperbolic equation. We emphasize work that remains to be done on these methods. 相似文献
20.
B. S. Goh 《Journal of Optimization Theory and Applications》1997,92(3):581-604
Existing algorithms for solving unconstrained optimization problems are generally only optimal in the short term. It is desirable to have algorithms which are long-term optimal. To achieve this, the problem of computing the minimum point of an unconstrained function is formulated as a sequence of optimal control problems. Some qualitative results are obtained from the optimal control analysis. These qualitative results are then used to construct a theoretical iterative method and a new continuous-time method for computing the minimum point of a nonlinear unconstrained function. New iterative algorithms which approximate the theoretical iterative method and the proposed continuous-time method are then established. For convergence analysis, it is useful to note that the numerical solution of an unconstrained optimization problem is none other than an inverse Lyapunov function problem. Convergence conditions for the proposed continuous-time method and iterative algorithms are established by using the Lyapunov function theorem. 相似文献