Local regularization of nonlinear Volterra equations of Hammerstein type (Q616665)

The paper is devoted to the numerical solution of the nonlinear Volterra equation \[ \int^t_0 k(t,s) g(s,u(s))\,ds=f(t),\quad t\in [0,1], \] with continuous \(k,g\) and \(f\). The authors develop a theory of local regularization for this equation for a wide class of kernels including kernels of convolution type. The implementation of the method is discussed, and numerical examples demonstrate that it can outperform the Lavrentiev regularization. Finally, the a posteriori selection of the regularization parameter is illustrated using a modified discrepancy principle.