A new spectral Galerkin method for solving the two dimensional hyperbolic telegraph equation

• Published in: Computers & mathematics with applications (1987) Vol. 72; no. 7; pp. 1926 - 1942
• Main Authors: Hesameddini, Esmail, Asadolahifard, Elham
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2016
• Subjects: Convergence; Dirichlet problem; Exponential convergence rate; Finite difference method; Galerkin methods; Hyperbolic telegraph equation; Mathematical analysis; Mathematical models; Sinc-Galerkin method; Spectra; Time discrete scheme; Two dimensional; Hyperbolic telegraph equation; Time discrete scheme; Exponential convergence rate; Sinc-Galerkin method
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/j.camwa.2016.08.003

Telegraph equation is more suitable than ordinary diffusion equation in modeling reaction–diffusion for several branches of sciences and engineering. In this paper, a new numerical technique is proposed for solving the second order two dimensional hyperbolic telegraph equation subject to initial and Dirichlet boundary conditions. Firstly, a time discrete scheme based on the finite difference method is obtained. Unconditional stability and convergence of this semi-discrete scheme are established. Secondly, a fully discrete scheme is obtained by the Sinc-Galerkin method and the problem is converted into a Sylvester matrix equation. Especially, when a symmetric Sinc-Galerkin method is used, the resulting matrix equation is a discrete ADI model problem. Then, the alternating-direction Sinc-Galerkin (ADSG) method is applied for solving this matrix equation. Also, the exponential convergence rate of Sinc-Galerkin method is proved. Finally, some examples are given to illustrate the accuracy and efficiency of proposed method for solving such types of differential equations compared to some other well-known methods.