A Regularization Method for the Elliptic Equation with Inhomogeneous Source. (4th March 2014)

• Record Type: Journal Article
• Authors: Nguyen, Tuan H.; Tran, Binh Thanh
• Other Names: Colombini F. Academic Editor.; Karakostas G. L. Academic Editor.
• Is Part Of: ISRN mathematical analysis. Volume 2014(2014)
• Publication Date: 2014-03-04
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Periodicals; 515
• DOI: 10.1155/2014/525636
• Languages: English
• ISSNs: 2090-4657

Abstract

Abstract : We consider the following Cauchy problem for the elliptic equation with inhomogeneous source in a rectangular domain with Dirichlet boundary conditions at x = 0 and x = π . The problem is ill-posed. The main aim of this paper is to introduce a regularization method and use it to solve the problem. Some sharp error estimates between the exact solution and its regularization approximation are given and a numerical example shows that the method works effectively.