Copyright © 2010 Ailin Qian et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the Cauchy problem for a modified Helmholtz equation, where the Cauchy data is given at x=1 and the solution is sought in the interval 0<x<1. A spectral method together with choice of regularization parameter is presented and error estimate is obtained. Combining the method of lines, we formulate regularized solutions which are stably convergent to the exact solutions.