On the functional-integral equation of Volterra type with weakly 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...

Numerical solution of a type of weakly singular nonlinear Volterra integral equation by Tau Method

‎In this paper‎, ‎a matrix based method is considered for the solution of a class of nonlinear Volterra integral equations with a kernel of the general form $s^{beta}(t-s)^{-alpha}G(y(s))$ based on the Tau method‎. ‎In this method‎, ‎a transformation of the independent variable is first introduced in order to obtain a new equation with smoother solution‎. ‎Error analysis of this method is also ...

An extrapolation method for a Volterra integral equation with weakly singular kernel

In this work we consider second kind Volterra integral equations with weakly singular kernels. By introducing some appropriate function spaces we prove the existence of an asymptotic error expansion for Euler’s method. This result allows the use of certain extrapolation procedures which is illustrated by means of some numerical examples. o 1997 Elsevier Science B.V.