An iterative boundary element method for solving the one-dimensional backward heat conduction problem

Discretized Tikhonov regularization by reproducing kernel Hilbert space for backward heat conduction problem

“…For the purpose of comparison with existing works [4,15,[20][21][22], the numerical experiments are conducted using the following typical benchmark test problem:…”

“…There are quite a large number of works devoted to stable numerical methods for BHCP. The following is a partial list of articles which contain numerical tests: the method of fundamental solutions [22], boundary element method [10,29], iterative boundary element method [21], inversion methods [18,20], Tikhonov regularization by maximum entropy principle [23], operatorsplitting methods [14], lattice-free finite difference method [12], Fourier regularization [7,8], quasi-reversibility [15,35], quasi-boundary regularization [4], modified methods [16,26], group preserving scheme [17], regularization by semi-implicit finite difference method [30], nonlinear multigrid gradient method [36], approximate and analytic inversion formula [19]. Comparisons of some inverse methods can be found in [5,24].…”

The truncation regularization method for identifying the initial value of heat equation on a spherical symmetric domain

“…A BHCP is severely ill-posed problem [1]. To overcome this difficulty, many scholars proposed some regularization techniques for the BHCP, such as the kernel-based method [2], the mollification method [3], the Fourier regularization method [4], optimal filtering method [5], the iterative method [6], the quasi-reversibility method [7][8][9], the central difference method [10], the filter regularization method [11], the method of fundamental solutions [12,13], the boundary element method [14,15], the group preserving scheme [16], modified Tikhonov regularization method [17], Quasi-boundary value method [18] and so on. But these references about BHCP, there are some drawbacks as follows: firstly, the regularization parameter is a prior choice rule, according to this choice rule, the parameter depends on the prior bound of the exact solution.…”

Quasi-Reversibility Regularization Method for Solving a Backward Heat Conduction Problem

“…Schröter and Tautenhahn [5] established an optimal error estimate for a special BHCP. Mera and Jourhmane used many numerical methods with regularization techniques to approximate the problem in [6][7][8], etc. A mollification method has been studied by Haö in [9].…”