Tikhonov Regularization by a Reproducing Kernel Hilbert Space for the Cauchy Problem for an Elliptic Equation Tikhonov Regularization by a Reproducing Kernel Hilbert Space for the Cauchy Problem for an Elliptic Equation
نویسندگان
چکیده
We propose a discretized Tikhonov regularization for a Cauchy problem for an elliptic equation by a reproducing kernel Hilbert space. We prove the convergence of discretized regularized solutions to an exact solution. Our numerical results demonstrate that our method can stably reconstruct solutions to the Cauchy problems even in severe cases of geometric configurations.
منابع مشابه
Reproducing Kernel Space Hilbert Method for Solving Generalized Burgers Equation
In this paper, we present a new method for solving Reproducing Kernel Space (RKS) theory, and iterative algorithm for solving Generalized Burgers Equation (GBE) is presented. The analytical solution is shown in a series in a RKS, and the approximate solution u(x,t) is constructed by truncating the series. The convergence of u(x,t) to the analytical solution is also proved.
متن کاملSolving multi-order fractional differential equations by reproducing kernel Hilbert space method
In this paper we propose a relatively new semi-analytical technique to approximate the solution of nonlinear multi-order fractional differential equations (FDEs). We present some results concerning to the uniqueness of solution of nonlinear multi-order FDEs and discuss the existence of solution for nonlinear multi-order FDEs in reproducing kernel Hilbert space (RKHS). We further give an error a...
متن کاملDiscretized Tikhonov regularization by reproducing kernel Hilbert space for backward heat conduction problem
In this paper we propose a numerical reconstruction method for solving a backward heat conduction problem. Based on the idea of reproducing kernel approximation, we reconstruct the unknown initial heat distribution from a finite set of scattered measurement of transient temperature at a fixed final time. Standard Tikhonov regularization technique using the norm of reproducing kernel is adopt to...
متن کاملReproducing Kernel Hilbert Space(RKHS) method for solving singular perturbed initial value problem
In this paper, a numerical scheme for solving singular initial/boundary value problems presented.By applying the reproducing kernel Hilbert space method (RKHSM) for solving these problems,this method obtained to approximated solution. Numerical examples are given to demonstrate theaccuracy of the present method. The result obtained by the method and the exact solution are foundto be in good agr...
متن کاملTikhonov Regularization Parameter in Reproducing Kernel Hilbert Spaces with Respect to the Sensitivity of the Solution
In our paper, we consider Tikhonov regularization in the reproducing Kernel Hilbert Spaces. In this space we derive upper and lower bound of the interval which contains the optimal value of Tikhonov regularization parameter with respect to the sensitivity of the solution without computing the singular values of the corresponding matrix. For the case of normalized kernel, we give an explicit for...
متن کامل