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

A numerical technique based on reproducing kernel methods for the exactsolution of linear Volterra integral equations system of the second kind isgiven. 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 W21[a,b]. It limits its application. Now, we modify the reproducing kernel method such that it can be more widelyapplicable. The n-term approximation solution obtained by the modifiedmethod is of high accuracy. The numerical example compared with othermethods shows that the modified method is more efficient