This paper is devoted to implementing the Legendre spectral collocation method to introduce numerical solutions of a certain class of fractional variational problems (FVPs). The properties of the Legendre polynomials and Rayleigh-Ritz method are used to reduce the FVPs to the solution of system of algebraic equations. Also, we study the convergence analysis. The obtained numerical results show ...

Recently, there has been an increasing interest in the study of singular and perturbed systems. In this paper we propose a collocation method for solving singularly perturbed Volterra integro-differential and Volterra integral equations. The method is based upon radial basis functions, using zeros of the shifted Legendre polynomial as the collocation points. The results of numerical experiments...

This paper investigates an adaptive wavelet collocation time domain method for the numerical solution of Maxwell’s equations. In this method a computational grid is dynamically adapted at each time step by using the wavelet decomposition of the field at that time instant. In the regions where the fields are highly localized, the method assigns more grid points; and in the regions where the fiel...

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...

Hough functions are the eigenfunctions of the Laplace tidal equation governing fluid motion on a rotating sphere with a resting basic state. Several numerical methods have been used in the past. In this paper, we compare two of those methods: normalized associated Legendre polynomial expansion and Chebyshev collocation. Both methods are not widely used, but both have some advantages over the co...

This paper first introduces Legendre wavelet bases and derives their rich properties. Then these properties are applied to estimation of approximation error upper bounded in spaces [ ] ( ) C 0,1 α and [ ] ( ) N C 0,1 +α by norms 2 ⋅ and 1 ⋅ , respectively. These estimate results are valuable to solve integral-differential equations by Legendre wavelet method.

An efficient Spectral Collocation method based on the shifted Legendre polynomials was applied to get solution of heat transfer of a micropolar fluid through a porous medium with radiation. A similarity transformation is applied to convert the governing equations to a system of nonlinear ordinary differential equations. Then, the shifted Legendre polynomials and their operational matrix of deri...

In this study, the thermal performance analysis of porous fin with temperature-dependent thermal conductivity and internal heat generation is carried out using Haar wavelet collocation method. The effects of various parameters on the thermal characteristics of the porous fin are investigated. It is found that as the porosity increases, the rate of heat transfer from the fin increases and the th...

‎a numerical technique based on the collocation method using legendre multiwavelets are‎‎presented for the solution of forced duffing equation‎. ‎the operational matrix of integration for‎‎legendre multiwavelets is presented and is utilized to reduce the solution of duffing equation‎‎to the solution of linear algebraic equations‎. ‎illustrative examples are included to demonstrate‎‎the validity...