Generalized Tikhonov regularization method for an inverse boundary value problem of the fractional elliptic equation

Abstract

Abstract This research studies the inverse boundary value problem for fractional elliptic equation of Tricomi–Gellerstedt–Keldysh type and obtains a condition stability result. To recover the continuous dependence of the solution on the measurement data, a generalized Tikhonov regularization method based on ill-posedness analysis is constructed. Under the a priori and a posterior selection rules for the regularization parameter, corresponding Hölder type convergence results are obtained. On this basis, this thesis verifies the simulation effect of the generalized Tikhonov method through numerical examples. The examples show that the method performs well in dealing with the problem under consideration.

Keywords

• Inverse boundary value problem
• Fractional elliptic equation
• Generalized Tikhonov regularization
• A priori and a posteriori convergence estimates
• Numerical simulation