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Title
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Reconstructing unknown nonlinear boundary conditions in a time-fractional inverse reaction–diffusion–convection problem
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Type
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JournalPaper
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Keywords
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Caputo’s fractional derivative, inverse problem, marching scheme, mollification, time-fractional reaction–diffusion– convection equation
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Abstract
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This paper has focused on unknown functions identification in nonlinear boundary conditions of an inverse problem of a time-fractional reaction–diffusion–convection equation. This inverse problem is generally ill-posed in the sense of stability, that is, the solution of problem does not depend continuously on the input data. Thus, a combination of the mollification regularization method with Gauss kernel and a finite difference marching scheme will be introduced to solve this problem. The generalized cross-validation choice rule is applied to find a suitable regularization parameter. The stability and convergence of the numerical method are investigated. Finally, two numerical examples are provided to test the effectiveness and validity of the proposed approach.
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Researchers
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ُSeddighe Banihashemi (Second Researcher), Afshin Babaei (First Researcher)
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