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Approximate Solutions of Fisher′s Type Equations with Variable Coefficients

Author

Listed:
  • A. H. Bhrawy
  • M. A. Alghamdi

Abstract

The spectral collocation approximations based on Legendre polynomials are used to compute the numerical solution of time‐dependent Fisher’s type problems. The spatial derivatives are collocated at a Legendre‐Gauss‐Lobatto interpolation nodes. The proposed method has the advantage of reducing the problem to a system of ordinary differential equations in time. The four‐stage A‐stable implicit Runge‐Kutta scheme is applied to solve the resulted system of first order in time. Numerical results show that the Legendre‐Gauss‐Lobatto collocation method is of high accuracy and is efficient for solving the Fisher’s type equations. Also the results demonstrate that the proposed method is powerful algorithm for solving the nonlinear partial differential equations.

Suggested Citation

  • A. H. Bhrawy & M. A. Alghamdi, 2013. "Approximate Solutions of Fisher′s Type Equations with Variable Coefficients," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:176730
    DOI: 10.1155/2013/176730
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    References listed on IDEAS

    as
    1. A. H. Bhrawy & L. M. Assas & M. A. Alghamdi, 2013. "Fast Spectral Collocation Method for Solving Nonlinear Time-Delayed Burgers-Type Equations with Positive Power Terms," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, August.
    2. D. Baleanu & A. H. Bhrawy & T. M. Taha, 2013. "Two Efficient Generalized Laguerre Spectral Algorithms for Fractional Initial Value Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Ali Ahmadian & Mohamed Suleiman & Soheil Salahshour, 2013. "An Operational Matrix Based on Legendre Polynomials for Solving Fuzzy Fractional-Order Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-29, June.
    4. D. Baleanu & A. H. Bhrawy & T. M. Taha, 2013. "A Modified Generalized Laguerre Spectral Method for Fractional Differential Equations on the Half Line," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, August.
    5. D. Baleanu & A. H. Bhrawy & T. M. Taha, 2013. "A Modified Generalized Laguerre Spectral Method for Fractional Differential Equations on the Half Line," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    6. A. H. Bhrawy & L. M. Assas & M. A. Alghamdi, 2013. "Fast Spectral Collocation Method for Solving Nonlinear Time‐Delayed Burgers‐Type Equations with Positive Power Terms," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    7. D. Baleanu & A. H. Bhrawy & T. M. Taha, 2013. "Two Efficient Generalized Laguerre Spectral Algorithms for Fractional Initial Value Problems," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, June.
    8. Ali Ahmadian & Mohamed Suleiman & Soheil Salahshour, 2013. "An Operational Matrix Based on Legendre Polynomials for Solving Fuzzy Fractional‐Order Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    9. Ferial Ghaemi & Robiah Yunus & Ali Ahmadian & Soheil Salahshour & Mohamed Suleiman & Shanti Faridah Saleh, 2013. "Application of Fuzzy Fractional Kinetic Equations to Modelling of the Acid Hydrolysis Reaction," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    10. Ferial Ghaemi & Robiah Yunus & Ali Ahmadian & Soheil Salahshour & Mohamed Suleiman & Shanti Faridah Saleh, 2013. "Application of Fuzzy Fractional Kinetic Equations to Modelling of the Acid Hydrolysis Reaction," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-19, September.
    11. 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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