in this paper, we present a method for solving the rst kind abel integral equation. in thismethod, the rst kind abel integral equation is transformed to the second kind volterraintegral equation with a continuous kernel and a smooth deriving term expressed by weaklysingular integrals. by using sidi's sinm - transformation and modi ed navot-simpson'sintegration rule, an algorithm for...

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.

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 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.

The present work approaches the problem of achieving the approximate solution of the second order initial value problems (IVPs) via its conversion into a Volterra integral equation of the second kind (VIE2). Therefore, we initially solve the IVPs using Runge–Kutta of the forth–order method (RK), and then convert it into VIE2, and apply the εmodified block–pulse functions (εMBPFs) and their oper...

In this paper, we present an efficient method for determining the solution of the stochastic second kind Volterra integral equations (SVIE) by using the Taylor expansion method. This method transforms the SVIE to a linear stochastic ordinary differential equation which needs specified boundary conditions. For determining boundary conditions, we use the integration technique. This technique give...