Showing 7 results for Nonlinear
Volume 9, Issue 1 (10-2010)
Abstract
This paper presents an appropriate numerical method to solve nonlinear Fredholm integro-differential equations with time delay. Its approach is based on the Taylor expansion. This method converts the integro-differential equation and the given conditions into the matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Taylor expansion coefficients, so that the solution of this system yields the Taylor expansion coefficients of the solution function. Then, the performance of the method is evaluated with some examples
Volume 10, Issue 1 (3-2010)
Abstract
In this paper, estimation of survey precision for nonlinear estimators is considered and an equation is presented based on sampling and nonsampling variances. Furthermore, by considering the response error model in surveys and the estimators of variance components, some relations are presented to computation of survey precision for nonlinear estimators. As an application case for the results, two typical data sets are considered and survey precisions of a nonlinear estimator are computed in the both data sets.
Esmaeil Babolian, Ar Vahidi,
Volume 11, Issue 2 (2-2011)
Abstract
In this paper, we conduct a comparative study between the homotopy perturbation method (HPM) and Adomian’s decomposition method (ADM) for analytic treatment of nonlinear Volterra integral equations, and we show that the HPM with a specific convex homotopy is equivalent to the ADM for these type of equations.
S Davaeefar, Yadollah Ordokhani,
Volume 13, Issue 2 (7-2013)
Abstract
In this article, the efficient numerical methods for finding solution of the linear and nonlinear Fredholm integral equations of the second kind on base of Bernstein multi scaling functions are being presented. In the beginning the properties of these functions, which are a combination of block-pulse functions on , and Bernstein polynomials with the dual operational matrix are presented. Then these properties are used for the purpose of conversion of the mentioned integral equation to a matrix equation that are compatible to a algebraic equations system. The imperative of the Bernstein multi scaling functions are, for the proper quantitative value of and have a high accuracy and specifically the relative errors of the numerical solutions will be minimum. The presented methods from the standpoint of computation are very simple and attractive and the numerical examples which were presented at the end shows the efficiency and accuracy of these methods.
Zahra Bahrami, Ali Mahdifar,
Volume 14, Issue 1 (4-2014)
Abstract
This paper aimed to investigate the relation between the coherent states and the wavelets. So first the standard, generalized and nonlinear coherent states were reviewed and then their properties were presented. As an example of the nonlinear coherent states, the coherent states of a two-dimensional harmonic oscillator on a flat space were examined. Using the Dirac notation, the admissibility condition of the mother wavelets was studied. Then by means of the resolution of the identity of the generalized coherent states and the admissibility condition of the wavelets, a systematic method was presented to calculate the polynomial wavelets. At the end, as an illustrative example, the polynomial wavelets were constructed by using the nonlinear coherent states on a flat space.
Azhdar Soleymanpour Bakefayat, Nader Dastranj,
Volume 17, Issue 40 (9-2015)
Abstract
In this paper, We Stabilize a subclass of nonlinear control systems by using neural networks and Zobov's theorem. Zobov’s Theorem is one of the theorems which indicates the conditions for the stability of a nonlinear systems with specific attraction region. We applied neural networks to approximate some functions mentioned in Zobov’s theorem, So as to find the controller of a nonlinear controlled system which is difficult task to find its law in mathematic manner. also we apply nelder meed optimization method to learning neural network. Finally, the effectiveness and the applicability of the proposed method are demonstrated by using some numerical examples.
Volume 18, Issue 44 (10-2009)
Abstract
Hybrid of rationalized Haar functions are developed to approximate the solution of the differential equations. The properties of hybrid functions which are the combinations of block-pulse functions and rationalized Haar functions are first presented. These properties together with the Newton-Cotes nodes are then utilized to reduce the differential equations to the solution of algebraic equations. The method is computationally attractive, and applications are demonstrated through illustrative examples.
