A Spectral Regularization Method for a Cauchy Problem of the Modified Helmholtz Equation. (13th June 2010) - Qian Qian, Ailin Ailin; Mao Mao, Jianfeng Jianfeng; Liu Liu, Lianghua Lianghua
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.