On a Non-linear Volterra Integral Equation with Singular Kernel

On the Volterra Integral Equation with Weakly Singular Kernel

A simple algorithm for solving the Volterra integral equation featuring a weakly singular kernel

There are many methods for numerical solutions of integral equations. In various branches of science and engineering, chemistry and biology, and physics applications integral equation is provided by many other authors. In this paper, a simple numerical method using a fuzzy, for the numerical solution of the integral equation with the weak singular kernel is provided. Finally, by providing three...

Solving a Volterra integral equation with weakly singular kernel in the reproducing kernel space

Abstract In this paper, we will present a new method for a Volterra integral equation with weakly singular kernel in the reproducing kernel space. Firstly the equation is transformed into a new equivalent equation. Its exact solution is represented in the form of series in the reproducing kernel space. In the mean time, the n-term approximation un(t) to the exact solution u(t) is obtained. Some...

Fredholm-volterra Integral Equation with Potential Kernel

A method is used to solve the Fredholm-Volterra integral equation of the first kind in the space L2(Ω)×C(0,T ),Ω = {(x,y) : √ x2+y2 ≤ a}, z = 0, and T <∞. The kernel of the Fredholm integral term considered in the generalized potential form belongs to the class C([Ω]×[Ω]), while the kernel of Volterra integral term is a positive and continuous function that belongs to the class C[0,T ]. Also in...

A Singular Nonlinear Volterra Integral Equation

This paper concerns the integral equation