Polynomial approximation of an inverse Cauchy problem for Helmholtz type equations - Aboud, Fatima; Jameel, Ibtihal Th; Hasan, Athraa F.; Mostafa, Baydaa Kh; Nachaoui, Abdeljalil (Advanced mathematical models & applications, 2022)
The objective of this paper is to solve numerically a Cauchy problem defined on a two-dimensional domain occupied by a material satisfying the Helmholtz type equations and verifying additional Cauchy-type boundary conditions on the accessible part of the boundary. A meshless numerical method using an approximation of the solution based on the polynomial expansion is applied. To confirm the efficiency of the proposed method, different examples were considered and the obtained linear system was solved using the well-known CG and CGLS algorithms.