THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Jin-Song Hu

,

Ju Chen

,

Li-Jia Yi

,

Ming-Fang Su

A TWO-LEVEL HIGH ACCURACY LINEARIZED DIFFERENCE SCHEME FOR THE BENJAMIN-BONA-MAHONY EQUATION

ABSTRACT
In this article we propose the anomalous diffusion models with respect to mono-tone increasing functions. The Riesz-type fractional order derivatives operators with respect to power-law function are considered based on the extended work of Riesz. Two models for the anomalous diffusion processes are given to describe the special behaviors in the complex media
KEYWORDS
anomalous diffusion, Riesz fractional derivative, Riesz-type fractional derivative with respect to monotone increasing function, Riesz-type fractional derivative with respect to power-law function
PAPER SUBMITTED: 2021-08-11
PAPER REVISED: 2021-08-27
PAPER ACCEPTED: 2021-09-01
PUBLISHED ONLINE: 2022-04-09
DOI REFERENCE: https://doi.org/10.2298/TSCI2202017H
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2022, VOLUME 26, ISSUE Issue 2, PAGES [1017 - 1024]
REFERENCES
  1. Benjamin, T. B., et al., Model Equations For Long Waves Non-Linear Dispersive System, Philosophical Transactions of the Royal Society London, 272 (1972), 1220, pp. 47-78
  2. Mei, M., Large-Time Behavior of Solution for Generalized Benjamin-Bona-Mahony-Burgers Equation, Non-linear Analysis: Theory Methods & Applications, 33 (1998), 7, pp. 699-714
  3. Mei, M., Decay Rates of Solutions for Generalized Benjamin-Bona-Mahony-Burgers Equation, Journal of Differential Equations, 158 (1999), 2, pp. 314-340
  4. Amick, C. J., et al., Decay of Solution of Some Non-linear Wave Equation, Journal of Differential Equations, 81 (1989), 1, pp. 1-49
  5. Bona, J. L., Dougalis, V. A., An iNitial and Boundary Value Problem for a Model Equation for Propagation Long Waves, Journal of Mathematical Analysis & Applications, 75 (1980), 2, pp. 503-522
  6. Wang, B. X., Attractors and Approximate Inertial Manifolds for the Generalized Benjamin-Bona-Mahony Equation, Mathematical Methods in the Applied Sciences, 20 (1997), 3, pp. 189-203
  7. Achouri, T., et al., On the Convergence of Difference Schemes for the Benjamin-Bona-Mahanoy (BBM) Equation, Applied Mathematics and Computation, 182 (2006), 2, pp. 999-1005
  8. Omrani, K., The Convergence of Fully Discrete Galerkin Approximations for the Benjamin-Bona-Mahony (BBM) Equation, Applied Mathematics and Computation, 180 (2006), 2, pp. 614-621
  9. Hu, J. S., Wang, Y. L., Quasi-Compact Difference Algorithm for Benjamin-Bona-Mahony Equations, (in Chinese), Journal of Southwest Normal University (Natural Science Edition), (2010), 2, pp. 35-64
  10. Zhang, Y., et al., Average Implicit Difference Schemes for Benjamin-Bona-Mahony Equations, (in Chinese), Journal of Sichuan University (Natural Science), 56 (2012), 3, pp. 955-959
  11. Che, H., et al., Numerical Analysis of A Linear-Implicit Average Scheme for Generalized Benjamin-Bona-Mahony-Burgers Equation, Journal of Applied Mathematics, 2012 (2012), ID 308410
  12. Xu, Y., et al., Mixed Finite Element Analysis for Dissipative SRLW Equations with Damping Term, Applied Mathematics, 38 (2015), 4, pp. 597-610
  13. Yu, X., et al., Numerical Method for the Time Optimal Control Problem Governed by the Benjamin-Bona-Mahony Equation, International Journal of Computational Science & Engineering, 13 (2016), 3, pp. 296-302
  14. Li, C., Linearized Difference Schemes for a BBM Equation with a Fractional Nonlocal Viscous Term, Applied Mathematics and Computation, 311 (2017), Oct., pp. 240-250
  15. Huang, J. T., et al., A High-Precision Non-Linear CN Difference Scheme for Solving BBM Equations, (in Chinese), Journal of Sichuan University (Natural Science), 56 (2019), 3, pp. 387-391
  16. Zhang, H., et al., A High-Precision Linear Difference Scheme for the Benjamin-Bona-Mahony Equation, (in Chinese), Journal of Sichuan University (Natural Science), 56 (2019), 5, pp. 813-818
  17. Zhou, Y., Application of Discrete Functional Analysis to the Finite Difference Method, International Academic Publishers, Beijing, China, 1990
  18. Zhou, Y. L., Application of Discrete Functional Analysis to the Finite Difference Methods, International Academic Publishers, Beijing, 1990
PDF VERSION [DOWNLOAD]
A two-level high accuracy linearized difference scheme for the Benjamin-Bona-Mahony equation

© 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