Quasi-reversibility and truncation methods to solve a Cauchy problem for the modified Helmholtz equation

The Weighted Generalized Solution Tikhonov Regularization Method for Cauchy Problem for the Modified Helmholtz Equation

“…The numerical results show that the proposed method is effective and stable. Compare with the method in [11], our method does not need the priori information.…”

“…Thus it is impossible to solve the problem using classical numerical methods and requires special techniques to be employed. In recent years, several techniques have been developed for it, such as the Landweber method with boundary element method (BEM) [8], the conjugate gradient method [7], the method of fundamental solutions(MFS) [3,9,14], the quasi-reversibility method and truncated method [10,11] and so on.…”

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

“…In [22,23], the authors used the truncation method to solve BHCP. In [24][25][26], the authors used the truncation method to solve a cauchy problem for the Helmholtz equation and the modified Helmholtz equation. In [27][28][29][30], the authors used the truncation method to identify the unknown source.…”

Optimal Error Bound and A Semi-discrete Difference Scheme for the Cauchy Problem of the Modified Helmholtz Equation

“…Therefore, it is necessary to study different highly efficient algorithms for solving it. In recent years, there are many special numerical methods to deal with this problem, such as the boundary element method [9], the method of fundamental solutions [10,17], the conjugate gradient method [11], the Landweber method [9], quasi-reversibility and truncation method [14], quasi-boundary and Tikhonov type regularization method [13,18], the Fourier regularization method [3,4] and so on [15]. In the present paper we will consider the following problem with inhomogeneous Dirichlet data in a strip domain:…”