THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Imtiaz Ahmad

,

Hijaz Ahmad

,

Mustafa Inc

PERFORMANCE OF MESHLESS METHOD OF LINES FOR THE SOLUTION OF THE GENERALIZED SEVENTH-ORDER KORTEWEG-DE VRIES EQUATION HAVING APPLICATIONS IN FLUID MECHANICS

ABSTRACT
In this article, we investigate the execution of a meshless method of line (MMOL) to solve general seventh-order Korteweg-de Vries (KdV7) equations numerically. The suggested meshless technique uses radial basis functions (RBF) for spatial derivatives and the Runge-Kutta (RK) method for time derivatives to solve the governing equation. To produce an efficient numerical solution, three different types of RBF are used. The method's output is successfully compared to the exact solution.
KEYWORDS
meshless method of line, radial basis functions, KdV7
PAPER SUBMITTED: 2022-07-11
PAPER REVISED: 2022-07-24
PAPER ACCEPTED: 2022-08-01
PUBLISHED ONLINE: 2023-04-08
DOI REFERENCE: https://doi.org/10.2298/TSCI23S1383A
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE Special issue 1, PAGES [383 - 388]
REFERENCES
  1. Malfliet, W., Solitary Wave Solutions of Non-Linear Wave Equations, Am. J. Phys., 60 (1992), 7, pp. 650-654
  2. Zabusky, N. J., Kruskal, M. D., Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States, Phys. Rev. Lett, 15 (1965), 6, 240
  3. Gardner, C. S., et al., Method for Solving the Korteweg-de Vries Equation, Phys. Rev. Lett., 19 (1967), 19, 1095
  4. Pomeau, Y., et al., Structural Stability of the Korteweg-de Vries Solitons under a Singular Perturbation, Phys. D: Non-Linear Phenomena, 31 (1988), 1, pp. 27-34
  5. Ito, M., An Extension of Non-Linear Evolution Equations of the KdV, mKdV-Type to Higher Orders, Journal Phys. Soc. Japan, 49 (1980), 2, pp. 771-778
  6. H. Jafari, A., et al., Application of He's Variational Iteration Method for Solving 7th Order Sawada-Kotera Equations, Appl. Math. Sci., 2 (2008), 9-12, pp. 471-477
  7. Wazwaz, A. M., The Hirota's Direct Method and the tanh-coth Method for Multiple-Soliton Solutions of the Sawada-Kotera-Ito 7th-Order Equation, Appl. Math. Comput., 199 (2008), 1, pp. 133-138
  8. Thounthong, P., et al., Symmetric Radial Basis Function Method for Simulation of Elliptic Partial Differential Equations, Mathematics, 6 (2018), 12, 327
  9. Ahmad, I., et al., Solution of Multi-Term Time-Fractional PDE Models Arising in Mathematical Biology and Physics by Local Meshless Method, Symmetry, 12 (2020), 7, 1195
  10. Ahmad, I., et al., Numerical Simulation of PDE by Local Meshless Differential Quadrature Collocation Method, Symmetry, 11 (2019), 3, 394
  11. Wang, F., et al., A Novel Meshfree Strategy for a Viscous Wave Equation with Variable Coefficients, Front. Phys., 9 (2021), 359
  12. Wang, F., et al., Gaussian Radial Basis Functions Method for Linear and Non-Linear Convection-Diffusion Models in Physical Phenomena, Open Phys., 19 (2021), 1, pp. 69-76
  13. Li, J. F., et al., Numerical Solution of Two-Term Time-Fractional PDE Models Arising in Mathematical Physics Using Local Meshless Method, Open Phys., 18 (2021), 1, pp. 1063-1072
  14. Khan, M. N., et al., Numerical Solution of Time-Fractional Coupled Korteweg-de Vries and Klein-Gordon Equations by Local Meshless Method, Pramana, 95 (2021), 1, pp. 1-13
  15. Srivastava H. M., et al., Numerical Simulation of 3-D Fractional-Order Convection-Diffusion PDE by a Local Meshless Method, Thermal Science, 25 (2021), 1A, pp. 347-358
  16. Ahmad, I., et al., Application of Local Meshless Method for the Solution of Two Term Time Fractional Order Multi-Dimensional PDE Arising in Heat and Mass Transfer, Thermal Science, 24 (2020), Suppl. 1, pp. S95-S105
  17. Abdelrahman, M.A.E., et al., Exact Solutions of the Cubic Boussinesq and Coupled Higgs System, Thermal Science, 24 (2020), Suppl. 1, pp. S333-S342
  18. Aliyu, A. I., et al., Adomian-Pade Approximate Solutions to the Conformable Non-Linear Heat Transfer Equation, Thermal Science, 23 (2019), Suppl. 1, pp. S235-S242
  19. Aliyu, A. I., et al., Approximate Solutions and Conservation Laws of the Periodic Base Temperature of Convective Longitudinal Fins in Thermal Conductivity, Thermal Science, 23 (2019), Suppl. 1, pp. S67-S273
PDF VERSION [DOWNLOAD]
Performance of meshless method of lines for the solution of the generalized seventh-order Korteweg-de Vries equation having applications in fluid mechanics

© 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