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Determination of control parameter in an inverse time fractional diffusion equation using a linearized fourth-order finite difference scheme | ||
| Journal of Mathematical Modeling | ||
| دوره 14، شماره 3، آبان 2026، صفحه 1053-1069 اصل مقاله (914.12 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2026.32796.2986 | ||
| نویسندگان | ||
| Akbar Mohebbi* 1؛ Behnam Salehi2 | ||
| 1Department of Applied Mathematics, Faculty of Mathematical Science, University of Kashan, Kashan, Iran | ||
| 2Department of Mathematics, Faculty of Mathematics, Statistics and Computer, Semnan University, Semnan, Iran | ||
| چکیده | ||
| The problem of finding the space- or time-dependent control parameter in partial differential equations has increasingly appeared in physical phenomena, for example, in the study of control theory, heat conduction process, and chemical diffusion. This study aims to construct an efficient numerical method to determine a time-dependent source term in a time fractional diffusion equation subject to over-specification at a point in the spatial domain. We use a second order scheme to discretize the equation in the time direction, then we replace the space derivative with a fourth-order compact finite difference approximation. We will construct a linearized difference scheme and prove the solvability, and unconditional stability of the proposed method. Due to the usually ill-posed nature of inverse problems, we examine the stability of the method with respect to perturbations of the data. We show that the proposed method achieves stable and accurate numerical approximations without using any regularization techniques. Numerical experiments show satisfactory results for problems with smooth, non-smooth, and discontinuous initial conditions. | ||
| کلیدواژهها | ||
| Control parameter؛ inverse problem؛ compact finite difference؛ stability؛ perturbation | ||
| مراجع | ||
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