An efficient matrix approach for two-dimensional diffusion and telegraph equations with Dirichlet boundary conditions

Somveer Singh, Vinita Devi, Emran Tohidi and Vineet Kumar Singh

Physica A: Statistical Mechanics and its Applications, 2020, vol. 545, issue C

Abstract: This article provides an efficient matrix approach by using Euler approximation for solving numerically the two-dimensional diffusion and telegraph equations subject to the Dirichlet boundary conditions. First, the main equation is reduced into partial integro-differential equations (PIDEs) and then operational matrices of differentiation and integration of Euler polynomials transform those PIDEs into algebraic generalized Sylvester equations. The inclusion of several test examples confirms the predicted accuracy and effectiveness of the method. Comparison of obtained numerical results is made with some earlier works (Zogheib and Tohidi, 2016, Singh et al., 2018).

Keywords: Two-dimensional diffusion equation; Two-dimensional telegraph equation; Euler polynomials; Operational matrices; Euler matrix method (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:545:y:2020:i:c:s0378437119321077

DOI: 10.1016/j.physa.2019.123784

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