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A New Tau Method for Solving Nonlinear Lane‐Emden Type Equations via Bernoulli Operational Matrix of Differentiation

Author

Listed:
  • E. Tohidi
  • Kh. Erfani
  • M. Gachpazan
  • S. Shateyi

Abstract

A new and efficient numerical approach is developed for solving nonlinear Lane‐Emden type equations via Bernoulli operational matrix of differentiation. The fundamental structure of the presented method is based on the Tau method together with the Bernoulli polynomial approximations in which a new operational matrix is introduced. After implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its solutions are the unknown Bernoulli coefficients. Also, under several mild conditions the error analysis of the proposed method is provided. Several examples are included to illustrate the efficiency and accuracy of the proposed technique and also the results are compared with the different methods. All calculations are done in Maple 13.

Suggested Citation

  • E. Tohidi & Kh. Erfani & M. Gachpazan & S. Shateyi, 2013. "A New Tau Method for Solving Nonlinear Lane‐Emden Type Equations via Bernoulli Operational Matrix of Differentiation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:850170
    DOI: 10.1155/2013/850170
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    References listed on IDEAS

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    1. Faezeh Toutounian & Emran Tohidi & Stanford Shateyi, 2013. "A Collocation Method Based on the Bernoulli Operational Matrix for Solving High-Order Linear Complex Differential Equations in a Rectangular Domain," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, April.
    2. Faezeh Toutounian & Emran Tohidi & Stanford Shateyi, 2013. "A Collocation Method Based on the Bernoulli Operational Matrix for Solving High‐Order Linear Complex Differential Equations in a Rectangular Domain," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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    Cited by:

    1. Emran Tohidi & M. M. Ezadkhah & S. Shateyi, 2014. "Numerical Solution of Nonlinear Fractional Volterra Integro‐Differential Equations via Bernoulli Polynomials," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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