A Modified Minimal Error Method for Solving Nonlinear Integral Equations via Multiscale Galerkin Methods. (2nd January 2022) - Yang, Hongqi; Zhang, Rong
Abstract: A modified minimal error method for nonlinear integral equations is established. Such method, combined with the discrepancy principle as stopping rule, is a regularization method, which yields convergence to an exact solution when the nonlinear operator F satisfies certain conditions. Furthermore, the convergence of the modified minimal error method via multiscale Galerkin methods is also proved. Finally, numerical results show the accuracy and efficiency of the proposed method.