Homotopy perturbation method is a well-known method for solving many functional equations such as differential equations, integral equations, integro-differential equations and so on. Applying this method needs some computations which are boring by hand. Therefore, creating a program to do all computations would be useful. In this work, a maple program is prepared to solve the second kind of Vo...

In this paper, we develop an efficient spectral method for numerically solving the nonlinear Volterra integral equation with weak singularity and delays. Based on symmetric collocation points, is illustrated, convergence results are obtained. end, two numerical experiments carried out to confirm theoretical results.

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...

This paper is concerned with the determination of nonlinear roll damping moments of ships including similar floating structures. Using the measured motion response data of ship’s roll motion, an inverse problem is formulated for the determination. The problem of damping determination is mathematically involved in a Volterra integral equation of the “first” kind between the roll responses and un...

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.