Solvability of the Nonlocal Inverse Parabolic Problem and Numerical Results
作者机构：Department of MathematicsCollege of ScienceJazan UniversityJazanSaudi Arabia Department of Mathematics and InformaticsLarbi Ben M’hidi UniversityOum El BouaghiAlgeria
出 版 物：《Computer Systems Science & Engineering》 (计算机系统科学与工程（英文）)
年 卷 期：2022年第40卷第3期
页 面：1109-1126页
核心收录：
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
主 题：Inverse problem nonlocal integral condition fixed point theorem Tikhonov regularization nonlinear optimization
摘 要：In this paper,we consider the unique solvability of the inverse problem of determining the right-hand side of a parabolic equation whose leading coefficient depends on time variable under nonlocal integral overdetermination *** obtain sufficient conditions for the unique solvability of the inverse *** existence and uniqueness of the solution of the inverse parabolic problem upon the data are established using the fixed point *** inverse problem appears extensively in the modelling of various phenomena in engineering and *** example,seismology,medicine,fusion welding,continuous casting,metallurgy,aircraft,oil and gas production during drilling and operation of *** addition,the numerical solution of the inverse problem is studied by using the Crank-Nicolson finite difference method together with the Tikhonov regularization to find a stable and accurate approximate solution of finite *** resulting nonlinear system of parabolic equation is solved computationally using the MATLAB subroutine *** analytical and numerically simulated noisy input data are *** root mean square error values for various noise levels for both continuous and discontinuous time-dependent heat source term are *** results presented for two examples show the efficiency of the computational method and the accuracy and stability of the numerical solution even in the presence of noise in the input ***,the choice of the regularization parameter is also discussed based on the trial and error technique.
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