Implicit extended discontinuous Galerkin scheme for solving singularly perturbed Burgers' equations

• Published in: Mathematical modelling and analysis Vol. 29; no. 1; pp. 1 - 22
• Main Authors: Khodayari-Samghabadi, Samaneh, Mondanizadeh, Maryam, Momeni-Masuleh, Sayed Hodjatollah
• Format: Journal Article
• Language: English
• Published: Vilnius Vilnius Gediminas Technical University 22.02.2024
• Subjects: backward Euler method; Basis functions; Burgers equation; discontinuous Galerkin method; Functions, Discontinuous; Functions, Implicit; Galerkin method; Laplace transforms; Ordinary differential equations; Perturbation (Mathematics); Polynomials; singularly perturbed Burgers’ equation; Stability analysis; Tests, problems and exercises; viscous Burgers’ equation; Iran; backward Euler method; discontinuous Galerkin method; viscous Burgers’ equation; singularly perturbed Burgers’ equation; stability analysis
• ISSN: 1392-6292; 1648-3510; 1648-3510
• DOI: 10.3846/mma.2024.16979

We present the implicit-modal discontinuous Galerkin scheme for solving the coupled viscous and singularly perturbed Burgers’ equations. This scheme overcomes overshoot and undershoots phenomena in the singularly perturbed Burgers’ equations. We present the stability analysis and obtain suitable ranges for penalty terms and time steps. Also, we gain the constant of trace inequality for the approximate function and its first derivatives based on Legendre basis functions. The numerical results have good agreement with the analytical and available approximate solutions.