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A Jacobi Collocation Method for Solving Nonlinear Burgers‐Type Equations

Author

Listed:
  • E. H. Doha
  • D. Baleanu
  • A. H. Bhrawy
  • M. A. Abdelkawy

Abstract

We solve three versions of nonlinear time‐dependent Burgers‐type equations. The Jacobi‐Gauss‐Lobatto points are used as collocation nodes for spatial derivatives. This approach has the advantage of obtaining the solution in terms of the Jacobi parameters α and β. In addition, the problem is reduced to the solution of the system of ordinary differential equations (SODEs) in time. This system may be solved by any standard numerical techniques. Numerical solutions obtained by this method when compared with the exact solutions reveal that the obtained solutions produce high‐accurate results. Numerical results show that the proposed method is of high accuracy and is efficient to solve the Burgers‐type equation. Also the results demonstrate that the proposed method is a powerful algorithm to solve the nonlinear partial differential equations.

Suggested Citation

  • E. H. Doha & D. Baleanu & A. H. Bhrawy & M. A. Abdelkawy, 2013. "A Jacobi Collocation Method for Solving Nonlinear Burgers‐Type Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:760542
    DOI: 10.1155/2013/760542
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    References listed on IDEAS

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    1. Ma, Zheng-Yi & Wu, Xiao-Fei & Zhu, Jia-Min, 2007. "Multisoliton excitations for the Kadomtsev–Petviashvili equation and the coupled Burgers equation," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 648-657.
    2. Tan, Yue & Xu, Hang & Liao, Shi-Jun, 2007. "Explicit series solution of travelling waves with a front of Fisher equation," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 462-472.
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    Cited by:

    1. Uthman O. Rufai & Precious Sibanda & Sicelo P. Goqo & Salma A. A. Ahmedai & Adeyinka S. Adeyemo, 2025. "Spectral Optimized Multiderivative Hybrid Block Method for Fitzhugh–Nagumo Equations," International Journal of Differential Equations, John Wiley & Sons, vol. 2025(1).
    2. Burcu Gürbüz & Mehmet Sezer & Coşkun Güler, 2014. "Laguerre Collocation Method for Solving Fredholm Integro‐Differential Equations with Functional Arguments," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    3. E. López-Sandoval & A. Mello & J. J. Godina-Nava & A. R. Samana, 2015. "Power Series Solution for Solving Nonlinear Burgers‐Type Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).

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