Based on the least square method, we proposed a new algorithm to obtain
the solution of the second kind regular and weakly singular
Volterra-Fredholm integral equations in reproducing kernel spaces. The
stability and uniform convergence of the algorithm are investigated in
details. Numerical experiments verify the theoretical findings.
Meanwhile this method is also applicable to the nonlinear Volterra
integral equations. Test problems which have non-smooth solutions are
also considered and our proposed method is efficient as some recent
Krylov subspace methods such as LSQR and LSMR.