In this paper, a nonlinear inverse problem of parabolic type, is considered. By reducing this inverse problem to a system of Volterra integral equations the existence, uniqueness, and stability of the solution will be shown.

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...

Integro-differential equations involving Volterra and Fredholm operators (VFIDEs) are used to model many phenomena in science engineering. Nonlocal boundary conditions more effective, some cases necessary, because they accurate measurements of the true state than classical (local) initial conditions. Closed-form solutions always desirable, not only efficient, but also can be valuable benchmarks...

In this work, we present a numerical method for solving nonlinear Fredholmand Volterra integral equations of the second kind which is based on the useof Block Pulse functions(BPfs) and collocation method. Numerical examplesshow eciency of the method.

in this paper the fixed point theorem of schauder is used to prove the existence of a continuous solution of the nonlinear fuzzy volterra integral equations. then using some conditions the uniqueness of the solution is investigated.

in this paper, a nonlinear inverse problem of parabolic type, is considered. by reducing this inverse problem to a system of volterra integral equations the existence, uniqueness, and stability of the solution will be shown.

this paper presents a comparison between variational iteration method (vim) and modfied variational iteration method (mvim) for approximate solution a system of volterra integral equation of the first kind. we convert a system of volterra integral equations to a system of volterra integro-di®erential equations that use vim and mvim to approximate solution of this system and hence obtain an appr...

a numerical method for solving nonlinear fredholm-volterra integral equations of general type is presented. this method is based on replacement of unknown function by truncated series of well known chebyshev expansion of functions. the quadrature formulas which we use to calculate integral terms have been imated by fast fourier transform (fft). this is a grate advantage of this method which has...

in this paper, we present a new computational technique for solving nonlinear fredholm integral equations of the second kind. this proposed method is based on galerkin method and is computationally very attractive. moreover, for reducing the operations in comparing similar works, we design our algorithm based on transformations of orthogonal polynomials in approximation coefficients calculating...

In this paper, we study the existence of solutions of some nonlinear Volterra integral equations by using the techniques of measures of noncompactness and the Petryshyn's fixed point theorem in Banach space. We also present some examples of the integral equation to confirm the efficiency of our results.