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.

in this paper, we propose a successive approximation method based on fuzzy wavelet like operator to approximate the solution of linear fuzzy fredholm integral equations of the second kind with arbitrary kernels. we give the convergence conditions and an error estimate. also, we investigate the numerical stability of the computed values with respect to small perturbations in the first iteration....

In this paper, we study polynomial spline collocation methods applied to a particular class of integral-algebraic equations of Volterra type. We analyse mixed systems of second and first kind integral equations. Global convergence and local superconvergence results are established.

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.

We will apply the successive approximation method forproving the Hyers--Ulam stability of a linear integral equation ofthe second kind.

we will apply the successive approximation method forproving the hyers--ulam stability of a linear integral equation ofthe second kind.

we develop and apply the product integration method to a large class of linear weakly singular volterra systems. we show that under certain sufficient conditions this method converges. numerical implementation of the method is illustrated by a benchmark problem originated from heat conduction.

We consider $ y(t) = g(t) + \int_{s 0}^t K(t, s, y(s))\, ds for 0 \le t T $, a nonlinear Volterra integral equation of the second kind, where K may be smooth or have an integrable singularity and g lies in space C^{m, \beta}(0, T] (for some positive integer m $) that is widely used work Vainikko his collaborators. The only analysis regularity solution y given by Brunner, Pedas Vainikko, Math. C...

Since the solution of a second-kind Volterra integral equation with weakly singular kernel has, in general, unbounded derivatives at the left endpoint of the interval of integration, its numerical solution by polynomial spline collocation on uniform meshes will lead to poor convergence rates. In this paper we investigate the convergence rates with respect to graded meshes, and we discuss the pr...