A Wavelet Method for Solving Backward Heat Conduction Problems
نویسندگان
چکیده
In this article, we consider the backward heat conduction problem (BHCP). This classical problem is more severely ill-posed than some other problems, since the error of the data will be exponentially amplified at high frequency components. The Meyer wavelet method can eliminate the influence of the high frequency components of the noisy data. The known works on this method are limited to the a priori choice of the regularization parameter. In this paper, we consider also a posteriori choice of the regularization parameter. The Hölder type stability estimates for both a priori and a posteriori choice rules are established. Moreover several numerical examples are also provided.
منابع مشابه
A regularization method for solving a nonlinear backward inverse heat conduction problem using discrete mollification method
The present essay scrutinizes the application of discrete mollification as a filtering procedure to solve a nonlinear backward inverse heat conduction problem in one dimensional space. These problems are seriously ill-posed. So, we combine discrete mollification and space marching method to address the ill-posedness of the proposed problem. Moreover, a proof of stability and<b...
متن کاملOptimal Pareto Parametric Analysis of Two Dimensional Steady-State Heat Conduction Problems by MLPG Method
Numerical solutions obtained by the Meshless Local Petrov-Galerkin (MLPG) method are presented for two dimensional steady-state heat conduction problems. The MLPG method is a truly meshless approach, and neither the nodal connectivity nor the background mesh is required for solving the initial-boundary-value problem. The penalty method is adopted to efficiently enforce the essential boundary co...
متن کاملDetermination of a Source Term in an Inverse Heat Conduction Problem by Radial Basis Functions
In this paper, we propose a technique for determining a source term in an inverse heat conduction problem (IHCP) using Radial Basis Functions (RBFs). Because of being very suitable instruments, the RBFs have been applied for solving Partial Dierential Equations (PDEs) by some researchers. In the current study, a stable meshless method will be pro- posed for solving an (I...
متن کاملA Numerical Method for Backward Inverse Heat Conduction Problem With two Unknown Functions
This paper considers a linear one dimensional inverse heat conduction problem with non constant thermal diffusivity and two unknown terms in a heated bar with unit length. By using the WKB method, the heat flux at the end of boundary and initial temperature will be approximated, numerically. By choosing a suitable parameter in WKB method the ill-posedness of solution will be improved. Finally, ...
متن کاملA novel computational procedure based on league championship algorithm for solving an inverse heat conduction problem
Inverse heat conduction problems, which are one of the most important groups of problems, are often ill-posed and complicated problems, and their optimization process has lots of local extrema. This paper provides a novel computational procedure based on finite differences method and league championship algorithm to solve a one-dimensional inverse heat conduction problem. At the beginning, we u...
متن کامل