Open Access Research Article

A Spectral Regularization Method for a Cauchy Problem of the Modified Helmholtz Equation

Ailin Qian*, Jianfeng Mao and Lianghua Liu

Author Affiliations

School of Mathematics and Statistics, Xianning College, Xianning, Hubei 437100, China

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Boundary Value Problems 2010, 2010:212056 doi:10.1155/2010/212056

Published: 13 June 2010

Abstract

We consider the Cauchy problem for a modified Helmholtz equation, where the Cauchy data is given at and the solution is sought in the interval . 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.