Open AccessSolving a source distribution in heat conduction equation by homotopy analysis method
Author(s) -
Bingxian Wang,
Mei Xu,
Chuanzhi Bai
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1707/1/012022
Subject(s) - homotopy analysis method , mathematics , regularization (linguistics) , homotopy , heat equation , diffusion equation , thermal conduction , convergence (economics) , mathematical optimization , distribution (mathematics) , sequence (biology) , mathematical analysis , computer science , physics , genetics , economy , artificial intelligence , biology , economic growth , pure mathematics , economics , thermodynamics , service (business)
The diffusion process from internal source is governed by the diffusion equation. The reconstruction of source distribution in heat conduction equation has been considered from final measurement data. The major difficulty in establishing any numerical algorithm for approximating the solution is the ill-posedness of the problem. Regularization procedures and recursive estimation algorithms should be developed. A homotopy-based iterative regularizing scheme has been proposed. The advantage of the proposed scheme is that under general assumptions on the exact initial distribution, the convergence of the homotopy sequence with any function in D φ as initial guess can always be guaranteed.