Solving the telegraph equation in 2-D and 3-D using generalized finite difference method (GFDM). (March 2020)

• Record Type: Journal Article
• Authors: Ureña, F.; Gavete, L.; Benito, J.J.; García, A.; Vargas, A.M.
• Is Part Of: Engineering analysis with boundary elements. Volume 112(2020)
• Page Start: 13
• Page End: 24
• Publication Date: 2020-03
• Subjects: Meshless methods -- Generalized finite difference method -- Telegraph equation; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2019.11.010
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: In this paper it is shown the application of the generalized finite difference method (GFDM) for solving numerically the Telegraph equation in two and three-dimensional spaces. The explicit time discretization is used and for approximating the spatial variables a GFDM is applied. The GFDM is a truly meshless method. The possibility of using a nodal method allowing irregular distribution of nodes in a natural way is one of the main advantages of the generalized finite difference method (GFDM). The stability condition using von Neumann method is done, which is provided in Theorem 1. Some numerical results have been reported and compared with the exact solutions for showing the accuracy and efficiency of the proposed numerical scheme.