An a posteriori truncation method for some Cauchy problems associated with Helmholtz-type equations

In this article, we investigate some Cauchy problems associated with Helmholtz-type equations in rectangle using the method of truncation. Not alike the previous literature, we propose to choose the regularization parameter by an a posteriori rule, with which we can obtain error estimates of Hölder-type between the exact solution and their regularized approximation. Numerical simulations show that the proposed scheme is effective and stable.