THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Zhen Fu

,

Zhen Guo

,

Jin-Song Hu

,

Zhi-Yuan Zhang

A DECOUPLED HIGH ACCURACY LINEAR DIFFERENCE SCHEME FOR SYMMETRIC REGULARIZED LONG WAVE EQUATION WITH DAMPING TERM

ABSTRACT
In this paper, the initial boundary value problem of the dissipative symmetric regularized long wave equation with a damping term is studied numerically, and a decoupled linearized difference scheme with a theoretical accuracy of O(τ2+h4)is proposed. Because the scheme removes the coupling between the variables in the original equation, the linearized difference scheme and the ex-plicit difference scheme can be used to solve the two variables in parallel, which greatly improves the efficiency of numerical solutions. To obtain the maximum norm estimation of numerical solutions, the mathematical induction and the discrete functional analysis methods are introduced directly to prove the convergence and the stability of the scheme. Numerical experiments have also verified the reliability of the proposed scheme.
KEYWORDS
damping, dissipation, symmetric regularized long wave equation, decoupled linearized difference scheme, convergence, stability
PAPER SUBMITTED: 2021-06-01
PAPER REVISED: 2021-07-20
PAPER ACCEPTED: 2021-07-29
PUBLISHED ONLINE: 2022-04-09
DOI REFERENCE: https://doi.org/10.2298/TSCI2202061F
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2022, VOLUME 26, ISSUE Issue 2, PAGES [1061 - 1068]
REFERENCES
  1. Clarkson, P. A., New Similarity Reductions and Painleve Analysis for the Symmetric Regularized Long Wave and Modified Benjamin-Bona-Mahoney Equations, Journal of Physics A Mathematical & General, 22 (1989), 18, pp. 3821-3848
  2. Shang, Y., Guo, B., Long Time Behavior of the Dissipative Generalized Symmetric Regularized Long Wave Equations, Partial Differential Equation, 15 (2002), 1, pp. 35-45
  3. Shang, Y., Guo, B., The Global Attractor of the Periodic Initial Value Problem for the Generalized Symmetric Regularized Long Wave Equation with Dissipation, (in Chinese), Acta Mathematica Scientica A, 23A (2003), 6, pp. 745-757
  4. Guo, B., Shang, Y., Approximate Inertial Manifolds to the Generalized Symmetric Regularized Long Wave Equations with Damping Term, Acta Mathematica Applicate Sinica, 19 (2003), 2, pp. 191-204
  5. Shang, Y. D., Guo, B. L., Exponential Attractor of Generalized Symmetric Regularized Long Wave Equation with Damping Term, (in Chinese), Appl. Math. and Mech., 26 (2005), 3, pp. 259-266
  6. Xu, Y., et al., Mixed Finite Element Analysis for Dissipative SRLW Equations with Damping Term, Applied Mathematics & Computation, 218 (2012), 29, pp. 4788-4797
  7. Hu, J., et al., A Linear Difference Scheme for Dissipative Symmetric Regularized Long Wave Equations with Damping Term, Boundary Value Problems, 2010 (2010), ID 781750
  8. Wei, J., et al., A Decoupling Linearized Difference Scheme for SRLW Equation with Damping Term, (in Chinese), Journal of Sichuan University (Natural Science Edition), 57 (2020), 5. pp. 847-851
  9. Zhou, J., Numerical Simulation of Generalized Symmetric Regularized Long-wave Equations with Damping Term, Intl. Journal of Digital Content Techn. and Its Applications, 7 (2013), 6, pp. 1142-1149
  10. Zhou, Y. L., Application of Discrete Functional Analysis to the Finite Difference Methods, International Academic Publishers, Beijing, China, 1990
PDF VERSION [DOWNLOAD]
A decoupled high accuracy linear difference scheme for symmetric regularized long wave equation with damping term

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence