A new least-squares-based reproducing kernel method for solving regular and weakly singular Volterra-Fredholm integral equations with smooth and nonsmooth solutions

Based on the least-squares method, we proposed a new algorithm to obtain the solution of the second kind of regular and weakly singular Volterra-Fredholm integral equations in reproducing kernel spaces. The stability and uniform convergence of the algorithm are investigated in detail. 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.