We give the explicit time description of four the following problems: dynamics and optimal dynamics for some important electromechanical system, Galerkin approximation for beam equation, computations of Melnikov function for perturbed Hamiltonian systems. All these problems are reduced to the problem of the solving of the systems of diierential equations with polynomial nonlinearities and with ...

Gauss–Legendre quadrature rules are of considerable theoretical and practical interest because of their role in numerical integration and interpolation. In this paper, a series expansion for the zeros of the Legendre polynomials is constructed. In addition, a series expansion useful for the computation of the Gauss–Legendre weights is derived. Together, these two expansions provide a practical ...

The main aim of this article is to generalize the Legendre operational matrix to the fractional derivatives and implemented it to solve the nonlinear multi-order fractional differential equations. In this approach, a truncated Legendre series together with the Legendre operational matrix of fractional derivatives are used. The main characteristic behind the approach using this technique is that...

We present constructive a priori error estimates forH 0 -projection into a space of polynomials on a one-dimensional interval. Here, “constructive” indicates that we can obtain the error bounds in which all constants are explicitly given or are represented in a numerically computable form. Using the properties of Legendre polynomials, we consider a method by which to determine these constants t...

in recent years, there has been greater attempt to find numerical solutions of differential equations using wavelet's methods. the following method is based on vector forms of haar-wavelet functions. in this paper, we will introduce one dimensional haar-wavelet functions and the haar-wavelet operational matrices of the fractional order integration. also the haar-wavelet operational matrice...

The Inverse Polynomial Reconstruction Method (IPRM) has been recently introduced by J.-H. Jung and B. Shizgal in order to remedy the Gibbs phenomenon, see [2], [3], [4], [5]. Their main idea is to reconstruct a given function from its n Fourier coefficients as an algebraic polynomial of degree n− 1. This leads to an n × n system of linear equations, which is solved to find the Legendre coeffici...

In recent years, more and people choose to travel by bus save time economic costs, but the problem of inaccurate arrival has become increasingly prominent. The reason is lack scientific planning departure time. This paper takes passenger flow as an important basis for interval, proposes a prediction method based on wavelet neural network, uses intelligent optimization algorithm study elastic in...

In this paper, the properties of the floor function has been used to find a function which is one on the interval [0, 1) and is zero elsewhere. The suitable dilation and translation parameters lead us to get similar function corresponding to the interval [a,b)[a,b). These functions and their combinations enable us to represent the stepwise functions as a function of floor function. We have appl...

This paper presents a forecasting method for time series. This method combines the wavelet analysis and several forecasting techniques such as Artificial Neural Networks (ANN), linear regression and random walk. The proposed method is tested using three real time series: the first contains historical data recorded during eight weeks from a WiMAX network and the other two are based on financial ...