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...

A generalization of the linear fractional integral equation u(t) = u0 + ∂−αAu(t), 1 < α < 2, which is written as a Volterra matrix–valued equation when applied as a pixel–by–pixel technique, has been proposed for image denoising (restoration, smoothing,...). Since the fractional integral equation interpolates a linear parabolic equation and a hyperbolic equation, the solution enjoys intermediat...

A new computational method based on Haar wavelets is proposed for solving multidimensional stochastic Itô-Volterra integral equations. The block pulse functions and their relations to Haar wavelets are employed to derive a general procedure for forming stochastic operational matrix of Haar wavelets. Then, Haar wavelets basis along with their stochastic operational matrix are used to approximate...

In this paper we discuss the existence of periodic solutions of discrete (and discretized) non-linear Volterra equations with finite memory. The literature contains a number of results on periodic solutions of non-linear Volterra integral equations with finite memory, of a type that arises in biomathematics. The “summation” equations studied here can arise as discrete models in their own right ...

It is known that to construct the stable multistep method with the higher order of accuracy for solving integral equation is actual. For this aim here we suggest some ways for the construction of hybrid methods for solving nonlinear Volterra integral equations of the second kind. Thus, foundational this extends stable hybrid method with higher order of accuracy. Note that the hybrid methods whi...

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 dierential and integro-dierential equations. for showing eciency of the method we give some numerical examples.

stefan problem with kinetics is reduced to a system of nonlinear volterra integral equations of second kind and newton's method is applied to linearize it. product integration solution of the linear form is found and sufficient conditions for convergence of the numerical method are given. an example is provided to illustrated the applicability of the method.

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 article, we give some results concerning the continuity of the nonlinear Volterra and Fredholm integral operators on the space L1[0,∞). Then by using the concept of measure of weak noncompactness, we prove an existence result for a functional integral equation which includes several classes of nonlinear integral equations. Our results extend some previous works.