in this study a numerical method is developed to solve the hammerstein integral equations. to this end the kernel has been approximated using the leastsquares approximation schemes based on legender-bernstein basis. the legender polynomials are orthogonal and these properties improve the accuracy of the approximations. also the nonlinear unknown function has been approximated by using the berns...

In this paper, we develop a framework to obtain approximate numerical solutions to ordi‌nary differential equations (ODEs) involving fractional order derivatives using Legendre wavelets approximations. The continues Legendre wavelets constructed on [0, 1] are uti‌lized as a basis in collocation method. Illustrative examples are included to demonstrate the validity and applicability of the techn...

In this paper, we consider the Legendre spectral Galerkin and Legendre spectral collocation methods to approximate the solution of Urysohn integral equation. We prove that the approximated solutions of the Legendre Galerkin and Legendre collocation methods converge to the exact solution with the same orders, O(n−r) in L2-norm and O(n 1 2 −r) in infinity norm, and the iterated Legendre Galerkin ...

in this article we decide to define a modified homotopy perturbation for solving non-linear integral equations. almost, all of the papers that was presented to solve non-linear problems by the homotopy method, they used from two non-linear and linear operators. but we convert a non-linear problem to two suitable non-linear operators also we use from appropriate bases functions such as legendre ...

A Legendre wavelet method is presented for numerical solutions of stochastic Volterra-Fredholm integral equations. The main characteristic of the proposed method is that it reduces stochastic Volterra-Fredholm integral equations into a linear system of equations. Convergence and error analysis of the Legendre wavelets basis are investigated. The efficiency and accuracy of the proposed method wa...

Abstract— This paper introduces a new set of orthogonal moments function hypergeometric based on the discrete Legendre polynomials. The Legendre moments can be effectively used as pattern features in the analysis of two-dimensional images. The implementation of moments proposed in this paper does not involve any numerical approximation, since the basis set is orthogonal in the discrete domain o...

in this paper, an effective technique is proposed to determine thenumerical solution of nonlinear volterra-fredholm integralequations (vfies) which is based on interpolation by the hybrid ofradial basis functions (rbfs) including both inverse multiquadrics(imqs), hyperbolic secant (sechs) and strictly positive definitefunctions. zeros of the shifted legendre polynomial are used asthe collocatio...