In this paper, the objective is to solve the functional differential equations in the following form using Legendre Wavelet Method (LWM), 0 f 0 u(t)=f(t ,u( t) ,u( (t))), t t t u( t)= (t), t t ′ α ≤ ≤   φ ≤  (1) where ƒ: [t0, tƒ]×R→R is a smooth function, α(t) is a continuous function on [t0, tƒ] and φ(t)∈C represents the initial point or the initial data. In the present paper, the most impo...

in this paper, a new method is investigated for model order reduction of high order systems based on moment matching technique. in this method, at first, full order model is expanded by legendre wavelet function which is included in orthogonal functions. a suitable fixed structure model is considered as reduced order model whose parameters are unknown. these unknown parameters are determined us...

problem (OCP) for systems governed by Volterra integro-differential (VID) equation is considered. The method is developed by means of the Legendre wavelet approximation and collocation method. The properties of Legendre wavelet together with Gaussian integration method are utilized to reduce the problem to the solution of nonlinear programming one. Some numerical examples are given to confirm t...

In this paper, we apply Legendre wavelet collocation method to obtain the approximate solution of nonlinear Stratonovich Volterra integral equations. The main advantage of this method is that Legendre wavelet has orthogonality property and therefore coefficients of expansion are easily calculated. By using this method, the solution of nonlinear Stratonovich Volterra integral equation reduces to...

in this paper, we present legendre wavelet method to obtain numerical solution of a singular integro-differential equation. the singularity is assumed to be of the cauchy type. the numerical results obtained by the present method compare favorably with those obtained by various galerkin methods earlier in the literature.

In this manuscript a new method is introduced for solving fractional differential equations. The fractional derivative is described in the Caputo sense. The main idea is to use fractional-order Legendre wavelets and operational matrix of fractional-order integration. First the fractional-order Legendre wavelets (FLWs) are presented. Then a family of piecewise functions is proposed, based on whi...

A numerical method based on Legendre multi-wavelets is applied for solving Lane-Emden equations which form Volterra integro-differential equations. The Lane-Emden equations are converted to Volterra integro-differential equations and then are solved by the Legendre multi-wavelet method. The properties of Legendre multi-wavelets are first presented. The properties of Legendre multi-wavelets are ...

This paper presents discontinuous Legendre wavelet Galerkin (DLWG) approach for solving onedimensional advection-diffusion equation (ADE). Variational formulation of this type equation and corresponding numerical fluxes are devised by utilizing the advantages of both the Legendre wavelet bases and discontinuous Galerkin (DG) method. The distinctive features of the proposed method are its simple...

In this paper, we present Legendre wavelet method to obtain numerical solution of a singular integro-differential equation. The singularity is assumed to be of the Cauchy type. The numerical results obtained by the present method compare favorably with those obtained by various Galerkin methods earlier in the literature.