On numerical experiments for Cauchy problems of elliptic operators

Over the last decade, there has been a considerable amount of new numerical methods being developed for solving the Cauchy problems of elliptic operators. In this paper, with some new classes of numerical experiments, we re-verify the conclusions in the review article [Wei T, Hon YC, Ling L. Method of fundamental solutions with regularization techniques for Cauchy problems of elliptic operators. Eng Anal Bound Elem 2007;31(4):373–85.] concerning the effectiveness of solving Cauchy problems with the method of fundamental solutions.