A computational method for solving Fredholm integral equations of the first kind is presented. The method utilizes Chebyshev wavelets constructed on the unit interval as basis in Galerkin method and reduces solving the integral equation to solving a system of algebraic equations. The properties of Chebyshev wavelets are used to make the wavelet coefficient matrices sparse which eventually leads...

In this paper, continuous Legendre multi-wavelets are utilized as a basis in a practical direct method to approximate the solutions of the Fredholm integral equations system. To begin with we describe the characteristic of Legendre multi-wavelets and will go on to indicate that through this method a system of Fredholm integral equations can be reduced to an algebraic equation. Finally, numerica...

An approximation method based on operational matrices of Bernstein polynomials used for the solution of Hammerstein integral equations. The operational matrices of these functions are utilized to reduce a nonlinear Hammerstein and Volterra Hammerstein integral equation to a system of nonlinear algebraic equations. The method is computationally very simple and attractive, and applications are de...

This paper generalizes Block-Pulse Functions method for solving systems of linear Volterra integral equations of the second kind. This method, using operational matrix associated with Block-Pulse Functions, reduces these types of equations to a linear lower triangular system of algebraic equations. Numerical examples are presented to illustrate the computational efficiency of the method.

A direct method for solving nonlinear two-dimensional Fredholm integral equations (FIE) of the second kind is presented. Using two-dimensional rationalized Haar (RH) functions, the numerical solution of these equations is reduced to solving a nonlinear system of algebraic equations. Numerical examples are presented to demonstrate the effectiveness of the proposed method.

In this paper, an efficient direct method based on Legendre wavelets is introduced to approximate the solution of Fredholm integral equations of the first kind. These basic functions are orthonormal and have compact support. The properties of the Legendre wavelets are utilized to convert the integral equations into a system of linear algebraic equations. The main characteristic of the method is...

A new computational method based on Wilson wavelets is proposed for solving a class of nonlinear stochastic It^{o}-Volterra integral equations. To do this a new stochastic operational matrix of It^{o} integration for Wilson wavelets is obtained. Block pulse functions (BPFs) and collocation method are used to generate a process to forming this matrix. Using these basis functions and their operat...

in this paper, we will compare a homotopy perturbation algorithm and taylor series expansin method for a system of second kind fredholm integral equations. an application of he’s homotopy perturbation method is applied to solve the system of fredholm integral equations. taylor series expansin method reduce the system of integral equations to a linear system of ordinary differential equation.

this paper gives an ecient numerical method for solving the nonlinear systemof volterra-fredholm integral equations. a legendre-spectral method based onthe legendre integration gauss points and lagrange interpolation is proposedto convert the nonlinear integral equations to a nonlinear system of equationswhere the solution leads to the values of unknown functions at collocationpoints.

The bending of a rectangular elastic plate under uniform distributed load and simply supported at the corners by equal-leg angles is studied analytically. The width of the supporting legs can be varied symmetrically about the plate axes giving mixed boundary conditions with supported and free edges. The solution is set up by using the Le'vy-Na'dai approach and the mixed boundary equation at the...