Материалы международной научной конференции «Уфимская осенняя математическая школа» (г. Уфа, 28 сентября – 1 октября 2022 г.). Том 2 / отв. редактор З.Ю. Фазуллин. - Уфа: РИЦ БашГУ, 2022. - 472 с.
NUMERICAL SOLUTION OF THE CAUCHY PROBLEM THREE-DIMENSIONAL HELMHOLTZ EQUATION
NUMERICAL SOLUTION OF THE CAUCHY PROBLEM THREE-DIMENSIONAL HELMHOLTZ EQUATION
In this paper, the application of the method of fundamental solutions
to the Cauchy problem associated with three-dimensional Helmholtz
equations is investigated. The resulting system of linear algebraic
equations is ill-conditioned and therefore its solution is regularized
by employing the zeroth-order Tikhonov functional, while the choice
of the regularization parameter is based on the L-curve method.