In the present work, by applying known Bernstein polynomials and their advantageous properties, we establish an efficient iterative algorithm to approximate the numerical solution of fuzzy Fredholm integral equations of the second kind. The convergence of the proposed method is given and the numerical examples illustrate that the proposed iterative algorithm are ‎valid.‎

In this paper, an iterative scheme for extracting approximate solutions of two dimensional Volterra-Fredholm integral equations is proposed. Considering some conditions on the kernel of the integral equation obtained by discretization of the integral equation, the convergence of the approximate solution to the exact solution is investigated. Several examples are provided to demonstrate the effi...

This paper involves extended b ? metric versions of a fractional differential equation, system equations and two-dimensional (2D) linear Fredholm integral equations. By various given hypotheses, exciting results are established in the setting an id="M2"> space. Thereafter, by making consequent use fixed point te...

in this paper, we propose a new method for the numerical solution of two-dimensional linear and nonlinear volterra integral equations of the first and second kinds, which avoids from using starting values. an existence and uniqueness theorem is proved and convergence isverified by using an appropriate variety of the gronwall inequality. application of the method is demonstrated for solving the ...

In this work, we present a computational method for solving second kindnonlinear Fredholm Volterra integral equations which is based on the use ofHaar wavelets. These functions together with the collocation method are thenutilized to reduce the Fredholm Volterra integral equations to the solution ofalgebraic equations. Finally, we also give some numerical examples that showsvalidity and applica...

in this paper, we propose a new method for the numerical solution of two-dimensional linear and nonlinear volterra integral equations of the first and second kinds, which avoids from using starting values. an existence and uniqueness theorem is proved and convergence isverified by using an appropriate variety of the gronwall inequality. application of the method is demonstrated for solving the ...

A new method is proposed for the numerical solution of linear mixed Volterra-Fredholm integral equations in one space variable. The proposed numerical algorithm combines the trapezoidal rule, for the integration in time, with piecewise polynomial approximation, for the space discretization. We extend the method to nonlinear mixed Volterra-Fredholm integral equations. Finally, the method is test...

We consider Volterra and Fredholm integral equations for functions with values in L-spaces. This includes corresponding problems for set-valued functions, fuzzy-valued functions and many others. We prove theorems of existence and uniqueness of the solution for such equations and suggest some algorithms for finding approximate solutions. We get initial results in the approximation of functions w...

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...

In this paper, we consider the numerical solutions of linear Fredholm integral equations of the second kind. The Quarter-Sweep Arithmetic Mean (QSAM) iterative method is applied to solve linear systems generated from discretization of the second kind linear Fredholm integral equations using quadrature method. In addition, the formulation and implementation of the proposed method to solve the pr...