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

In this paper, we will present a new method for a Volterra integralequation 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 $u_{n}(t)$ to the exact solution $u(t)$ is obtained. Some numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method are compared with the exact solution of each example and are found to be in good agreement with each other.