A Spectral Regularization Method for a Cauchy Problem of the Modified Helmholtz Equation. (13th June 2010)

• Record Type: Journal Article
• Authors: Qian, Ailin; Mao, Jianfeng; Liu, Lianghua
• Other Names: Messaoudi Salim Academic Editor.
• Is Part Of: Boundary value problems. Volume 2010(2010)
• Publication Date: 2010-06-13
• Subjects: Boundary value problems -- Periodicals; Boundary value problems; Electronic journals; Periodicals; 515.35
• DOI: 10.1155/2010/212056
• Languages: English
• ISSNs: 1687-2762

Abstract

Abstract : We consider the Cauchy problem for a modified Helmholtz equation, where the Cauchy data is given atx = 1 and the solution is sought in the interval0 < 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.