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Numerical solution of a class of advection-reaction-diffusion system

ABSTRACT
In this article, the barycentric interpolation collocation methods is proposed for solving a class of nonlinear advection-reaction-diffusion system. Compared with other methods, the numerical experiment shows the barycentric interpolation collocation method is a high precision method to solve the advection- reaction-diffusion system.
KEYWORDS
PAPER SUBMITTED: 2018-08-03
PAPER REVISED: 2018-11-29
PAPER ACCEPTED: 2019-02-21
PUBLISHED ONLINE: 2019-05-26
DOI REFERENCE: https://doi.org/10.2298/TSCI180803217C
REFERENCES
  1. Tamsir, M., et al., Numerical Computation of Nonlinear Fisher's Reaction-Diffusion Equation with Exponential Modified Cubic B-Spline Differential Quadrature Method, International Journal of Applied and Computational Mathematics, 4(2018), 3, pp.1-6
  2. Dhiman, N., Tamsir, M., A Collocation Technique Based on Modified Form of Trigonometric Cubic B-Spline Basis Functions for Fishers Reaction-Diffusion Equation, Multidiscipline Modeling in Materials and Structures, 14 (2018), 5, pp.923- 939
  3. He, J. H., Approximate Solution of Nonlinear Differential Equations with Convolution Product Nonlinearities, Computer Methods in Applied Mechanics and Engineering, 167(1998), 1-2, pp. 69-73
  4. He, J. H., Homotopy Perturbation Method: A New Nonlinear Analytical Technique, Appl. Math. Comput, 135(2003), pp. 73-79
  5. Yang, X. J., A New Integral Transform Operator for Solving the Heat-diffusion Problem, Applied Mathematics Letters, 64(2017), Jan., pp.193-197
  6. Ambrosio D., et al., Adapted Numerical Methods for Advection-Reaction-Diffusion Problems Generating Periodic Wavefronts, Computers & Mathematics with Applications, 74 (2017), pp. 1029-1042
  7. Jiwari, R., et al., Numerical Simulation to Capture the Pattern Formation of Coupled Reaction-Diffusion Models, Chaos, Solitons and Fractals, 103 (2017), 5, pp. 422-439
  8. Li, S. P., et al., Barycentric Interpolation Collocation Method for Nonlinear Problems, Beijing, National Defense Industry Press, 2015
  9. Li, S. P., et al., High-Precision Non-Grid Center of Gravity Interpolation Collocation Method: Algorithm, Program and Engineering Application, Beijing, Science Press, 2012
  10. Zhou X. F., et al., Numerical Simulation of a Class of Hyperchaotic System Using Barycentric Lagrange Interpolation Collocation Method, Complexity, 2019(2019), ID 1739785
  11. Liu, F. F., et al., Barycentric Interpolation Collocation Method for Solving the Coupled Viscous Burgers' Equations, International Journal of Computer Mathematics, 95(2018), pp. 2162-2173
  12. Wu, H. C., et al., Numerical Solution of a Class of Nonlinear Partial Differential Equations by Using Barycentric Interpolation Collocation Method, Mathematical Problems in Engineering, 2018(2018) , ID 7260346, pp.1-150
  13. Du M. J., Li J. M., et al., Numerical Simulation of a Class of Three-Dimensional Kolmogorov Model with Chaotic Dynamic Behavior by Using Barycentric Interpolation Collocation Method, Complexity, 2019(2019), ID 3426974, pp.1-10
  14. D'Ambrosio, R., et al., Adapted Numerical Methods for Advection-Reaction-Diffusion Problems Generating Periodic Wavefronts, Computers & Mathematics with Applications, 74 (2017), 5, pp. 1029-1042