in this paper, a nonlinear volterra-fredholm integral equation of the first kind is solved by using the homotopy analysis method (ham). in this case, the first kind integral equation can be reduced to the second kind integral equation which can be solved by ham. the approximate solution of this equation is calculated in the form of a series which its components are computed easily. the accuracy...

In this paper it is shown that the use of‎ ‎uniform meshes leads to optimal convergence rates provided that‎ ‎the analytical solutions of a particular class of‎ ‎Fredholm-Volterra integral equations (FVIEs) are smooth‎.

In this paper we intend to offer new numerical methods to solvethe fuzzy Fredholm- Volterra integral equations of the firstkind $(FVFIE-1)$. Some examples are investigated to verify convergence results and to illustrate the efficiently of the methods.  

Since various problems in science and engineering fields can be modeled by nonlinear Volterra-Fredholm integral equations, the main focus of this study is to present an effective numerical method for solving them. This method is based on the hybrid functions of Legendre polynomials and block-pulse functions. By using this approach, a nonlinear Volterra-Fredholm integral equation reduces to a no...

We consider nonlinear integral equations of Fredholm and Volterra type with respect to functions having values in L-spaces. Such class of equations includes set-valued integral equations, fuzzy integral equations and many others. We prove theorems of existence and uniqueness of the solutions for such equations and investigate data dependence of their solutions.

An ecient method, based on the Legendre wavelets, is proposed to solve thesecond kind Fredholm and Volterra integral equations of Hammerstein type.The properties of Legendre wavelet family are utilized to reduce a nonlinearintegral equation to a system of nonlinear algebraic equations, which is easilyhandled with the well-known Newton's method. Examples assuring eciencyof the method and its sup...

In this paper, Adomian method has been applied to approximate the solution of fuzzy volterra-fredholm integral equation. That, by using parametric form of fuzzy numbers, a fuzzy volterra-fredholm integral equation has been converted to a system of volterra-fredholm integral equation in crisp case. Finally, the method is explained with illustrative examples.

This paper describes an approximating solution, based on Lagrange interpolation and spline functions, to treat functional integral equations of Fredholm type and Volterra type. This method can be extended to functional differential and integro-differential equations. For showing efficiency of the method we give some numerical examples.

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.

in this paper, existence theorems for the fuzzy volterra-fredholm integral equations of mixed type (fvfiemt) involving fuzzy number valued mappings have been investigated. then, by using banach's contraction principle, sufficient conditions for the existence of a unique solution of fvfiemt are given. finally, illustrative examples are presented to validate the obtained results.