This paper gives an efficient numerical method for solving the nonlinear system of Volterra-Fredholm integral equations. A Legendre-spectral method based on the Legendre integration Gauss points and Lagrange interpolation is proposed to convert the nonlinear integral equations to a nonlinear system of equations where the solution leads to the values of unknown functions at collocation points.

Properties of the hybrid of block-pulse functions and Lagrange polynomials based on the Legendre-Gauss-type points are investigated and utilized to define the composite interpolation operator as an extension of the well-known Legendre interpolation operator. The uniqueness and interpolating properties are discussed and the corresponding differentiation matrix is also introduced. The appl...

Department of Mathematics and Sciences Dhofar University, Salalah Oman [email protected] Abstract Legendre wavelets methods are commonly used for the numerical solution of integral equations. In this paper, we apply the Legendre wavelets method to approximate the solution of fractional integro-differential equations. Numerical examples are also presented to demonstrate the validity of the method....

We introduce a new and efficient Chebyshev-Legendre Galerkin method for elliptic problems. The new method is based on a Legendre-Galerkin formulation, but only the Chebyshev-Gauss-Lobatto points are used in the computation. Hence, it enjoys advantages of both the LegendreGalerkin and Chebyshev-Galerkin methods.

We give the explicit time description of the following problems: dynamics and optimal dynamics for nonlinear (polynomial) dynamical systems, Galerkin approximations for some class of partial diierential equations and routes to chaos in Melnikov function approach to the perturbations of Hamiltonian systems. The rst three problems and a part of the fourth one are reduced to the problem of the sol...

In this paper, an efficient method to obtain the elements current distribution for a non uniformly spaced array is presented. For a given far field pattern, after sampling the array factor the proposed method uses the least mean square error technique to solve the system of equations rather than solving the previously published Legendre function method. It’s shown that the average side lob leve...

We give the explicit time description of the following problems: dynamics of storage rings, optimal dynamics for some important electromechanical system, Galerkin approximation for beam oscillations in liquid, computations of Melnikov functions for perturbed Hamiltonian systems. All these problems are reduced to the problem of the solving of the systems of diierential equations with polynomial ...

The continuous wavelet transform is already a well established procedure for analysing data. Its main advantages over the classical Fourier transform are its local and multiresolution nature, which provide the interesting properties of a mathematical microscope. Its theory is well known in the case of the line and plane. However, the representation and analysis of signals in non-Euclidean geome...

properties of the hybrid of block-pulse functions and lagrange polynomials based on the legendre-gauss-type points are investigated and utilized to define the composite interpolation operator as an extension of the well-known legendre interpolation operator. the uniqueness and interpolating properties are discussed and the corresponding differentiation matrix is also introduced. the applicabili...