Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Determination of Unknown Time-Dependent Heat Source in Inverse Problems under Nonlocal Boundary Conditions by Finite Integration Method

  • Areena Hazanee (Department of Mathematics and Computer Science, Faculty of Science and Technology, Prince of Songkla University, Pattani Campus) ;
  • Nifatamah Makaje (Department of Mathematics and Computer Science, Faculty of Science and Technology, Prince of Songkla University, Pattani Campus)
  • Received : 2022.08.15
  • Accepted : 2024.01.02
  • Published : 2024.06.30
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Abstract

In this study, we investigate the unknown time-dependent heat source function in inverse problems. We consider three general nonlocal conditions; two classical boundary conditions and one nonlocal over-determination, condition, these genereate six different cases. The finite integration method (FIM), based on numerical integration, has been adapted to solve PDEs, and we use it to discretize the spatial domain; we use backward differences for the time variable. Since the inverse problem is ill-posed with instability, we apply regularization to reduce the instability. We use the first-order Tikhonov's regularization together with the minimization process to solve the inverse source problem. Test examples in all six cases are presented in order to illustrate the accuracy and stability of the numerical solutions.

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Acknowledgement

This research was fully financially supported by the Research Career Development Grant 2017 under the Office of Research Affairs, Faculty of Science and Technology, Prince of Songkla University, Thailand. Authors would like to thank Assoc. Prof. Dr. Seppo Karrila for valuable comments/suggestions on this paper.

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