A numerical approach for solving an inverse parabolic problem with unknown control function. (2015)

• Record Type: Journal Article
• Authors: Pourgholi, Reza; Abtahi, Morteza; Tabasi, S. Hashem
• Is Part Of: International journal of computational science and engineering. Volume 10:Number 4(2015)
• Page Start: 395
• Page End: 401
• Publication Date: 2015
• Subjects: inverse heat conduction -- stability -- fundamental solution method -- Tikhonov regularisation method -- L-curve method -- inverse parabolic problem -- unknown control function -- unknown boundary conditions; Computer science -- Mathematics -- Periodicals; Computer simulation -- Mathematical aspects -- Periodicals; Computational intelligence -- Periodicals; 004.015105
• Languages: English
• ISSNs: 1742-7185

Abstract

In this paper, we will first study the existence and uniqueness of the solution for a one dimensional inverse heat conduction problem (IHCP) via an auxiliary problem. Then the present work is motivated by desire to obtain numerical approach for solving this IHCP. Our method begins with the utilisation of some transformations. These transformations allow us to eliminate an unknown term from parabolic equation to obtain an inverse parabolic problem with two unknown boundary conditions. To solve this inverse problem, we use the fundamental solution method. The effectiveness of the algorithm is illustrated by numerical example.