In this work, we propose a new method for solving Volterra integral equations. The technique is based on the Chebyshev spectral collocation method. application of proposed leads equation to system algebraic equations that are easy solve. Some examples presented and compared with some methods in literature illustrate ability technique. results demonstrate more efficient, convergent, accurate exa...

If the solution of an integral equation can be expanded in the form of a Chebyshev series, the equation can be transformed into an infinite set of algebraic equations in which the unknowns are the coefficients of the Chebyshev series. The algebraic equations are solved by standard iterative procedures, in which it is not necessary to determine beforehand how many coefficients are significant. T...

Let c be a linear functional defined by its moments c(x) = ci for i = 0, 1, . . .. We proved that the nonlinear functional equations P (t) = c(P (x)P (x + t)) and P (t) = c(P (x)P (xt)) admit polynomial solutions which are the polynomials belonging to the family of formal orthogonal polynomials with respect to a linear functional related to c. Other types of nonlinear functional equations whose...

Urysohn integral equation is one of the most applicable topics in both pure and applied mathematics. The main objective of this paper is to solve the Urysohn type Fredholm integral equation. To do this, we approximate the solution of the problem by substituting a suitable truncated series of the well known Legendre polynomials instead of the known function. After discretization of the problem o...

the first integral method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. this method can be applied to non integrable equations as well as to integrable ones. in this paper, the first integral method is used to construct exact solutions of the 2d ginzburg-landau equation.

in this paper, using the tools involving measures of noncompactness and darbo fixed point theorem forcondensing operator, we study the existence of solutions for a large class of generalized nonlinear quadraticfunctional integral equations. also, we show that solutions of these integral equations are locally attractive.furthermore, we present an example to show the efficiency and usefulness of ...

in this paper, we studied the numerical solution of nonlinear weakly singular volterra-fredholm integral equations by using the product integration method. also, we shall study the convergence behavior of a fully discrete version of a product integration method for numerical solution of the nonlinear volterra-fredholm integral equations. the reliability and efficiency of the proposed scheme are...

This study presents a collocation approach for the numerical integration of multi-order fractional differential equations with initial conditions in Caputo sense. The problem was transformed from its integral form into system linear algebraic equations. Using matrix inversion, are solved and their solutions substituted approximate equation to give results. effectiveness precision method were il...

In this paper, an optimal control of quadratic performance index with nonlinear constrained is presented. The sine-cosine wavelet operational matrix of integration and product matrix are introduced and applied to reduce nonlinear differential equations to the nonlinear algebraic equations. Then, the Newton-Raphson method is used for solving these sets of algebraic equations. To present ability ...

The homotopy perturbation method is a powerful device for solving a wide variety of problems arising in many scientific applications. In this paper, we investigate several integral equations by using T-stability of the Homotopy perturbation method investigates for solving integral equations. Some illustrative examples are presented to show that the Homotopy perturbation method is T-stable for s...