In this paper, we propose the triangular orthogonal functions as a basis functions
 for solution of weakly singular Volterra integral equations second
 kind. Powerful properties these and some operational matrices
 are utilized in direct method to reduce equation to
 algebraic equations. The presented does not need any integration
 obtaining constant coefficients. is co...

The Volterra delay integral equations have numerous applications in various branches of science, including biology, ecology, physics and modeling of engineering and natural sciences. In many cases, it is difficult to obtain analytical solutions of these equations. So, numerical methods as an efficient approximation method for solving Volterra delay integral equations are of interest to many res...

In this paper, we will compare a Homotopy perturbation algorithm and Taylor series expansin method for a system of second kind Fredholm integral equations. An application of He’s homotopy perturbation method is applied to solve the system of Fredholm integral equations. Taylor series expansin method reduce the system of integral equations to a linear system of ordinary differential equation.

The paper presents an iterative numerical method for approximating solutions of two-dimensional Fredholm–Volterra integral equations the second kind. As these arise in many applications, there is a constant need accurate, but fast and simple to use approximations their solutions. proposed here uses successive Mann type suitable cubature formula. Mann’s procedure known converge faster than class...

The basic linear, Volterra integral equation of the first kind with a weakly singular kernel is solved via a Galerkin approximation. It is shown that the approximate solution is a sum with the first term being the solution of Abel's equation and the remaining terms computable as components of the solution of an initialvalue problem. The method represents a significant decrease in the normal num...

T The nonlinear and linear Volterra-Fredholm ordinary integral equations arise from various physical and biological models. The essential features of these models are of wide applicable. These models provide an important tool for modeling a numerous problems in engineering and science [6, 7]. Modelling of certain physical phenomena and engineering problems [8, 9, 10, 11, 12] leads to two-dimens...

The equation for the orbit of the classical Lotka-Volterra oscillator is solved for one of two variables in terms of the other by using two inverse functions of x exp(x). Moreover, the period of the orbit is expressed as an integral, which is approximated numerically by Gauss-Tschebyscheff integration rule of the first kind.

In this paper, we consider the nonlocal FredholmVolterra integral equation of the second kind, with continuous kernels. We consider three different numerical methods,the Trapezoidal rule, Simpson rule and Collocation method to reduce the nonlocal F-VIE to a nonlocal algebraic system of equations. The algebraic system is computed numerically, when the historical memory of the problem (nonlocal f...