Open AccessIdentification of spacewise dependent right-hand side in two dimensional parabolic equation
Author(s) -
Ling De Su,
В. И. Васильев
Publication year - 2021
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 - 10.1088/1742-6596/2092/1/012019
Subject(s) - inverse problem , mathematics , function (biology) , conjugate gradient method , variable (mathematics) , inverse , parabolic partial differential equation , mathematical analysis , field (mathematics) , operator (biology) , iterative method , mathematical optimization , partial differential equation , geometry , pure mathematics , biochemistry , chemistry , repressor , evolutionary biology , gene , transcription factor , biology
In this paper numerical solution of the inverse problem of determining a spacewise dependent right-hand side function in two dimensional parabolic equation is considered. Usually, the right-hand side function dependent on spatial variable is obtained from measured data of the solution at the final time point. Many mathematical modeling problems in the field of physics and engineering will encounter the inverse problems to identify the right-hand terms. When studying an inverse problem of identifying the spacewise dependent right-hand function, iterative methods are often used. We propose a new conjugate gradient method based on the constructed self-adjoint operator of the equation for numerical solution of the function and numerical examples illustrate the efficiency and accuracy.