Ashyralyev, Allaberen; Sazaklioglu, Ali UgurSazaklıoğlu, Ali Uğur2024-06-252024-06-2520170163-0563https://acikarsiv.thk.edu.tr/handle/123456789/1299In the present paper, a time-dependent source identification problem subject to an integral overdetermination is considered. Stability estimates for this differential problem are established. Furthermore, a first and a second order of accuracy difference schemes are proposed for the approximate solution of this problem. Stability and almost coercive stability estimates for these difference schemes are established. Additionally, some illustrative numerical results are provided.EnglishFinite difference method; identification problem; inverse problem; stability theory; 65M06; 65M32; 34K20RIGHT-HAND SIDE; PARABOLIC EQUATION; NUMERICAL-SOLUTION; SOLVABILITY; STABILITY; SPACEArticle