In this paper, we consider a variant of projected Tikhonov regularization method for solving Fredholm integral equations of the first kind. We give a theoretical analysis of this method in the Hilbert space L 2 (a, b) setting and establish some convergence rates under certain regularity assumption on the exact solution and the kernel k(·, ·). Some numerical results are also presented.
In this paper, we are concerned with the problem of approximating a solution of an ill-posed biparabolic problem in the abstract setting. In order to overcome the instability of the original problem, we propose a regularizing strategy based on the Kozlov-Maz'ya iteration method. Finally, some other convergence results including some explicit convergence rates are also established under a priori bound assumptions on the exact solution.MSC: Primary 47A52; secondary 65J22
In this paper, we are interested in the inverse problem for the biharmonic equation posed on a rectangle, which is of great importance in many areas of industry and engineering. We show that the problem under consideration is ill-posed; therefore, to solve it, we opted for a regularization method via modified auxiliary boundary conditions. The numerical implementation is based on the application of the semidiscrete finite difference method for a sequence of well-posed direct problems depending on a small parameter of regularization. Numerical results are performed for a rectangle domain showing the effectiveness of the proposed method. KEYWORDS auxiliary boundary conditions, biharmonic equation, convergence estimate, ill-posed problems, plates, regularization MSC CLASSIFICATION 35J40; 31B30; 35B45; 74K20; 47A52 Abbreviations: BHP, biharmonic problem; MABCM, modified auxiliary boundary conditions method; QBVM, quasi-boundary value method. wileyonlinelibrary.com/journal/mma
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