Solving a system of linear Volterra integral equations using the new reproducing kernel method

In this paper, we present a new numerical technique to obtain the approximation solution for linear Volterra integral equations of the second kind based on reproducing kernel theory. The approximation solution is expressed by n-term summation of reproducing kernel functions. The merit of the new method includes (1) it is easy to implement this method; (2) high accuracy. The numerical examples compared with other methods show that the new method is more efficient.