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A new domain decomposition algorithm for generalized Burger’s–Huxley equation based on Chebyshev polynomials and preconditioning

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  • Javidi, M.
  • Golbabai, A.

Abstract

In this study, we use the spectral collocation method using Chebyshev polynomials for spatial derivatives and fourth order Runge–Kutta method for time integration to solve the generalized Burger’s–Huxley equation (GBHE). To reduce round-off error in spectral collocation (pseudospectral) method we use preconditioning. Firstly, theory of application of Chebyshev spectral collocation method with preconditioning (CSCMP) and domain decomposition on the generalized Burger’s–Huxley equation presented. This method yields a system of ordinary differential algebric equations (DAEs). Secondly, we use fourth order Runge–Kutta formula for the numerical integration of the system of DAEs. The numerical results obtained by this way have been compared with the exact solution to show the efficiency of the method.

Suggested Citation

  • Javidi, M. & Golbabai, A., 2009. "A new domain decomposition algorithm for generalized Burger’s–Huxley equation based on Chebyshev polynomials and preconditioning," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 849-857.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:2:p:849-857
    DOI: 10.1016/j.chaos.2007.01.099
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    References listed on IDEAS

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    7. Javidi, M. & Golbabai, A., 2008. "Exact and numerical solitary wave solutions of generalized Zakharov equation by the variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 309-313.
    8. Abulwafa, E.M. & Abdou, M.A. & Mahmoud, A.A., 2006. "The solution of nonlinear coagulation problem with mass loss," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 313-330.
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    1. Korkut, Sıla Övgü, 2023. "An accurate and efficient numerical solution for the generalized Burgers–Huxley equation via Taylor wavelets method: Qualitative analyses and Applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 209(C), pages 324-341.
    2. Somayeh Abdi-Mazraeh & Ali Khani & Safar Irandoust-Pakchin, 2020. "Multiple Shooting Method for Solving Black–Scholes Equation," Computational Economics, Springer;Society for Computational Economics, vol. 56(4), pages 723-746, December.
    3. Duan, Yali & Kong, Linghua & Zhang, Rui, 2012. "A lattice Boltzmann model for the generalized Burgers–Huxley equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 625-632.
    4. Hassan, M.M. & Abdel-Razek, M.A. & Shoreh, A.A.-H., 2015. "Explicit exact solutions of some nonlinear evolution equations with their geometric interpretations," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 243-252.

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