Solving a System of Linear Volterra Integral Equations Using the Modified Reproducing Kernel Method

Abstract

A numerical technique based on reproducing kernel methods for the exact solution of linear Volterra integral equations system of the second kind is given. The traditional reproducing kernel method requests that operator a satisfied linear operator equation $Au=f$, is bounded and its image space is the reproducing kernel space $W_2^1[a,b]$. It limits its application. Now, we modify the reproducing kernel method such that it can be more widely applicable. The n-term approximation solution obtained by the modified method is of high accuracy. The numerical example compared with other methods shows that the modified method is more efficient.