共查询到20条相似文献,搜索用时 46 毫秒
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We investigate local and semi-local convergence of the combined Newton-Kurchatov method under the classical and generalized Lipschitz conditions for solving nonlinear equations. The convergence order of the method is examined and the uniqueness ball for the solution of the nonlinear equation is proved. Numerical experiments are conducted on test problems. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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We study a local and a semilocal convergence of the two-step method for solving nonlinear equations with a nondifferentiable operator. Its method is based on two methods of order of convergence . We carry out the numerical research on test problems and do the comparison of obtained results. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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S.M. Shakhno 《Journal of Computational and Applied Mathematics》2009,231(1):222-235
We study an iterative method with order for solving nonlinear operator equations in Banach spaces. Algorithms for specific operator equations are built up. We present the received new results of the local and semilocal convergence, in case when the first-order divided differences of a nonlinear operator are Hölder continuous. Moreover a quadratic nonlinear majorant for a nonlinear operator, according to the conditions laid upon it, is built. A priori and a posteriori estimations of the method’s error are received. The method needs almost the same number of computations as the classical Secant method, but has a higher order of convergence. We apply our results to the numerical solving of a nonlinear boundary value problem of second-order and to the systems of nonlinear equations of large dimension. 相似文献
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S. M. Shakhno 《PAMM》2004,4(1):650-651
We apply the method of linear interpolation of Kurchatov to solve nonlinear operator equations in Banach spaces. Using the principle of majorants of L. V. Kantorovich, we study the semilocal convergence of method of Kurchatov. Quadratic order of convergence of this method is determined. A priori and a posteriori estimations of method's error are received. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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In this paper, we prove that the order of a new secant-like method presented recently with the so-called order of 2.618 is only 2.414. Some mistakes in the derivation leading to such a conclusion are pointed out. Meanwhile, under the assumption that the second derivative of the involved function is bounded, the convergence radius of the secant-like method is given, and error estimates matching its convergence order are also provided by using a generalized Fibonacci sequence. 相似文献
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William La Cruz 《Applied mathematics and computation》2010,217(1):11-24
A derivative-free residual method for solving nonlinear operator equations in real Hilbert spaces is discussed. This method uses in a systematic way the residual as search direction, but it does not use first order information. Furthermore a convergence analysis and numerical results of the new method applied to nonlinear integral equations using symbolic computation are presented. 相似文献
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Lawrence C. Evans 《Israel Journal of Mathematics》1980,36(3-4):225-247
We use similar functional analytic methods to solve (a) a fully nonlinear second order elliptic equation, (b) a Hamilton-Jacobi
equation, and (c) a functional/partial differential equation from plasma physics. The technique in each case is to approximate
by the solutions of simpler problems, and then to pass to limits using a modification of G. Minty’s device to the spaceL
∞.
Alfred P. Sloan fellow 1979–1981.
Supported in part by NSF grant MCS 77-01952. 相似文献
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Fadi Awawdeh 《Numerical Algorithms》2010,54(3):395-409
Solving systems of nonlinear equations is a relatively complicated problem for which a number of different approaches have
been proposed. In this paper, we employ the Homotopy Analysis Method (HAM) to derive a family of iterative methods for solving
systems of nonlinear algebraic equations. Our approach yields second and third order iterative methods which are more efficient
than their classical counterparts such as Newton’s, Chebychev’s and Halley’s methods. 相似文献
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In this paper,we consider the following nonlinear wave equations:(■~2φ)/(■t~2)-(■~2φ)/(■x~2)+μ~2φ+v~2x~2φ+f(|φ|~2)φ=0,(■~2x)/(■t~2-(■~2X)/(■X~2)+α~2x+α~2x+v~2x|φ|~2+g(X)=0with the periodic-initial conditions:φ(x-π,t)=φ(x+π,t),x(x-π,t)=x(x+v,t),φ(x,0)=■_0(x),φ_t(x,0)=■_1(x),X(x,0)=■_0(x),x_t(x,0)=■_1(x),-∞相似文献
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An iterative method for finding a solution of the equation f(x)=0 is presented. The method is based on some specially derived quadrature rules. It is shown that the method can give better results than the Newton method. 相似文献
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This paper outlines a reliable strategy for solving nonlinear Volterra-Fredholm integro-differential equations. The modified form of Adomian decomposition method is found to be fast and accurate. Numerical examples are presented to illustrate the accuracy of the method. 相似文献
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Fuyi Li Zhanping Liang Qi Zhang Yuhua Li 《Journal of Mathematical Analysis and Applications》2007,327(2):1010-1028
In this paper, the existence of sign-changing solutions for nonlinear operator equations is discussed by using the topological degree and fixed point index theory. The main theorems are some new three-solution theorems which are different from the famous Amann's and Leggett-Williams' three-solution theorems as well as the results in [F. Li, G. Han, Generalization for Amann's and Leggett-Williams' three-solution theorems and applications, J. Math. Anal. Appl. 298 (2004) 638-654]. These three solutions are all nonzero. One of them is positive, another is negative, and the third one is a sign-changing solution. Furthermore, the theoretical results are successfully applied to both integral and differential equations. 相似文献
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In this paper, we develop an inexact-Newton method for solving nonsmooth operator equations in infinite-dimensional spaces. The linear convergence and superlinear convergence of inexact-Newton method under some conditions are shown. Then, we characterize the order of convergence in terms of the rate of convergence of the relative residuals. The present inexact-Newton method could be viewed as the extensions of previous ones with same convergent results in finite-dimensional spaces. 相似文献
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We present an approach to constructing stable methods for solving nonlinear operator equations in Banach space without anyassumptions on the regularity of the operator. The approach is based on the linearization of the equation and the use of aregularization algorithm to find an approximate solution of the linearized equation at each iteration. The local convergence of proposed methods is proved and the estimations of the rate of convergence are established, provided that solution satisfies a sourcewise representation condition. The case of noisy data is also analysed. 相似文献
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Summary. We present a semi-discrete method for constructing approximate solutions to the initial value problem for the -dimensional convection-diffusion equation . The method is based on the use of operator splitting to isolate the convection part and the diffusion part of the equation.
In the case , dimensional splitting is used to reduce the -dimensional convection problem to a series of one-dimensional problems. We show that the method produces a compact sequence
of approximate solutions which converges to the exact solution. Finally, a fully discrete method is analyzed, and demonstrated
in the case of one and two space dimensions.
ReceivedFebruary 1, 1996 / Revised version received June 24, 1996 相似文献
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Varsha Daftardar-Gejji Hossein Jafari 《Journal of Mathematical Analysis and Applications》2006,316(2):753-763
An iterative method for solving nonlinear functional equations, viz. nonlinear Volterra integral equations, algebraic equations and systems of ordinary differential equation, nonlinear algebraic equations and fractional differential equations has been discussed. 相似文献