Generalized-Fractional Tikhonov-Type Method for the Cauchy Problem of Elliptic Equation
MATHEMATICS(2020)
摘要
This article researches an ill-posed Cauchy problem of the elliptic-type equation. By placing the a-priori restriction on the exact solution we establish conditional stability. Then, based on the generalized Tikhonov and fractional Tikhonov methods, we construct a generalized-fractional Tikhonov-type regularized solution to recover the stability of the considered problem, and some sharp-type estimates of convergence for the regularized method are derived under the a-priori and a-posteriori selection rules for the regularized parameter. Finally, we verify that the proposed method is efficient and acceptable by making the corresponding numerical experiments.
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关键词
Cauchy problem,elliptic equation,regularization method,a-priori and a-posteriori convergence estimates,numerical simulation
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