AN ALTERNATING PROCEDURE WITH DYNAMIC RELAXATION FOR CAUCHY PROBLEMS GOVERNED BY THE MODIFIED HELMHOLTZ EQUATION

Karzan A. Berdawood , Abdeljalil Nachaoui (1) , Rostam Saeed , Mourad Nachaoui , Fatima Aboud

1 LMJL - Laboratoire de Mathématiques Jean Leray

In this paper, two relaxation algorithms on the Dirichlet Neumann boundary condition, for solving the Cauchy problem governed to the Modified Helmholtz equation are presented and compared to the classical alternating iterative algorithm. The numerical results obtained using our relaxed algorithm and the finite element approximation show the numerical stability, consistency and convergence of these algorithms. This confirms the efficiency of the proposed methods.

Mots clés: Inverse Cauchy problem; modified Helmholtz equation; relaxed alternating iterative method; numerical simulation.

Domaines: Mathématiques [math]; Analyse numérique [math.NA]; Optimisation et contrôle [math.OC]

Karzan A. Berdawood, Abdeljalil Nachaoui, Rostam Saeed, Mourad Nachaoui, Fatima Aboud. AN ALTERNATING PROCEDURE WITH DYNAMIC RELAXATION FOR CAUCHY PROBLEMS GOVERNED BY THE MODIFIED HELMHOLTZ EQUATION. Advanced Mathematical Models & Applications, 2020, 5 (1), pp.131-139. ⟨hal-02589163⟩