Liviu Marin

TL;DR: The method of fundamental solutions (MFS) is a relatively new method for the numerical solution of boundary value problems and initial/boundary value problems governed by certain partial differential equations as discussed by the authors.

TL;DR: In this article, the application of the method of fundamental solutions to the Cauchy problem associated with two-dimensional Helmholtz-type equations is investigated, where the resulting system of linear algebraic equations is ill-conditioned and therefore its solution is regularized by employing the first-order Tikhonov functional, while the choice of the regularization parameter is based on the L-curve method.

TL;DR: In this paper, the application of fundamental solutions to the Cauchy problem for steady-state heat conduction in two-dimensional functionally graded materials (FGMs) is investigated, and the convergence and the stability of the method with respect to increasing the number of source points and the distance between the source points between the boundary of the solution domain, and decreasing the amount of noise added into the input data, respectively, are analyzed.

TL;DR: In this paper, the iterative algorithm proposed by Kozlov et al. for obtaining approximate solutions to the ill-posed Cauchy problem for the Helmholtz equation is analyzed.

TL;DR: In this article, an iterative algorithm based on the conjugate gradient method (CGM) in combination with the boundary element method (BEM) for obtaining stable approximate solutions to the Cauchy problem for Helmholtz-type equations is analyzed.