THERMAL SCIENCE

International Scientific Journal

NUMERICAL SIMULATION OF THE GENERALIZED BURGER'S-HUXLEY EQUATION VIA TWO MESHLESS METHODS

ABSTRACT
Numerical solution of the generalized Burger's-Huxley equation is established utilizing two effective meshless methods namely: local differential quadrature method and global method of line. Both the proposed meshless methods used radial basis functions to discretize space derivatives which convert the given model equation system of ODE and then we have utilized the Euler method to get the required numerical solution. Numerical experiments are carried out to check the efficiency and accuracy of the suggested meshless methods.
KEYWORDS
PAPER SUBMITTED: 2022-09-01
PAPER REVISED: 2022-11-03
PAPER ACCEPTED: 2022-11-14
PUBLISHED ONLINE: 2023-01-21
DOI REFERENCE: https://doi.org/10.2298/TSCI22S1463A
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2022, VOLUME 26, ISSUE Special issue 1, PAGES [463 - 468]
REFERENCES
  1. Satsuma, J., et al., Topics in Soliton Theory and Exactly Solvable Non-linear Equations, World Scientific, Singapore, Singapore 1987
  2. Wang, X. Y., et al., Solitary Wave Solutions of the Generalized Burger's-Huxley equation, Journal Phys. A: Math. Gen., 23 (1990), 3, pp. 271-274
  3. 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
  4. Hussain, Z., et al., Extension of Optimal Homotopy Asymptotic Method with Use of Daftardar-Jeffery Polynomials to Hirota-Satsuma Coupled System of Korteweg de Vries Equations, Open Phys., 18 (2020), 1, pp. 916-924
  5. 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
  6. Ahmad, I., et al., Numerical Simulation of PDE by Local Meshless Differential Quadrature Collocation Method, Symmetry, 11 (2019), 3, 394
  7. Thounthong, P., et al., Symmetric Radial Basis Function Method for Simulation of Elliptic Partial Differential Equations, Mathematics, 6 (2018), 12, 327
  8. Wang, F., et al., A Novel Meshfree Strategy for a Viscous Wave Equation with Variable Coefficients, Front. Phys., 9 (2021), 359
  9. 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
  10. 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
  11. Srivastava H. M., et al., Numerical Simulation of 3-D Fractional-Order Convection-Diffusion PDE by a Local Meshless Method, Thermal Science, 25 (2020), 1A, pp. 347-358
  12. 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), 1, pp. 95-105
  13. Shen, Q., A Meshless Method of Lines for the Numerical Solution of KdV Equation Using Radial Basis Functions, Eng. Anal. Bound. Elem., 33 (2009), 10, pp. 1171-1180
  14. Haq, S., et al., Meshless Method of Lines for the Numerical Solution of Generalized Kuramoto-Sivashinsky Equation, Appl. Math. Comput., 217 (2010), 6, pp. 2404-2413
  15. Ulutas, E., et al., Bright, Dark, and Singular Optical Soliton Solutions for Perturbed Gerdjikov-Ivanov Equation, Thermal Science, 25 (2021), Special Issue 2, pp. S151-S156
  16. Ulutas, E., et al., Exact Solutions of Stochastic KdV Equation with Conformable Derivatives in white Noise Environment, Thermal Science, 25 (2021), Special Issue 2, pp. S143-S149
  17. Yildirim, E. N., et al., Reproducing Kernel Functions and Homogenizing Transforms, Thermal Science, 25 (2021), Special Issue 2, pp. S9-S18
  18. Abdelrahman, M. A. E., et al., Exact Solutions of the Cubic Boussinesq and the Coupled Higgs Systems, Thermal Science, 24 (2020), Suppl. 1, pp. S333-S342

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