Determination of temperature distribution and control parameter in a two-dimensional parabolic inverse problem with overspecified data

doi:10.1088/1674-1056/20/10/100201

Abstract In this paper, we present a new algorithm to solve a two-dimensional parabolic inverse problem with a source parameter, which appears in many physical phenomena. A linearized compact difference scheme for this problem is constructed using the finite difference method. The discretization accuracy is second-order in time and fourth-order in space. We obtain the unique solvability and present an alternating direction implicit algorithm to solve this difference scheme. The results of numerical experiments are presented to demonstrate the accuracy of this algorithm.

Keywords: control parameter temperature distribution finite difference scheme solvability

Received: 13 July 2010
Revised: 23 May 2011
Accepted manuscript online:

PACS:	02.30.Jr	(Partial differential equations)
	02.30.Zz	(Inverse problems)
	02.60.Cb	(Numerical simulation; solution of equations)
	02.70.Bf	(Finite-difference methods)

Fund: Project supported by the Natural Science Foundation of Shandong Province of China (Grant No. ZR2009AL012) and the Science and Technology Program of Education Bureau of Shandong Province, China (Grant No. J09LA12).

Cite this article:

Li Fu-Le(李福乐) and Zhang Hong-Qian(张洪谦) Determination of temperature distribution and control parameter in a two-dimensional parabolic inverse problem with overspecified data 2011 Chin. Phys. B 20 100201

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Determination of temperature distribution and control parameter in a two-dimensional parabolic inverse problem with overspecified data

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