Tikhonov regularization method for identifying the space-dependent source for time-fractional diffusion equation on a columnar symmetric domain
Fan Yang, Pan Zhang, Xiaoxiao Li, Xin-Yi Ma
Abstract
Abstract In this paper, we deal with the inverse problem of identifying the unknown source of time-fractional diffusion equation on a columnar symmetric domain. This problem is ill-posed. Firstly, we establish the conditional stability for this inverse problem. Then the regularization solution is obtained by using the Tikhonov regularization method and the error estimates are derived under the a priori and a posteriori choice rules of the regularization parameter. Three numerical examples are presented to illustrate the validity and effectiveness of our method.
Topics & Concepts
Tikhonov regularizationRegularization (linguistics)MathematicsA priori and a posterioriInverse problemBackus–Gilbert methodOrdinary differential equationApplied mathematicsPartial differential equationRegularization perspectives on support vector machinesMathematical analysisDiffusion equationDifferential equationComputer scienceEconomicsService (business)EconomyArtificial intelligenceEpistemologyPhilosophyFractional Differential Equations SolutionsNumerical methods in inverse problemsNumerical methods in engineering