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Numerical Solution of Nonlinear Fractional Volterra Integro‐Differential Equations via Bernoulli Polynomials

Author

Listed:
  • Emran Tohidi
  • M. M. Ezadkhah
  • S. Shateyi

Abstract

This paper presents a computational approach for solving a class of nonlinear Volterra integro‐differential equations of fractional order which is based on the Bernoulli polynomials approximation. Our method consists of reducing the main problems to the solution of algebraic equations systems by expanding the required approximate solutions as the linear combination of the Bernoulli polynomials. Several examples are given and the numerical results are shown to demonstrate the efficiency of the proposed method.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:162896
    DOI: 10.1155/2014/162896
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    References listed on IDEAS

    as
    1. 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, Hindawi, vol. 2013, pages 1-9, May.
    2. F. Toutounian & Emran Tohidi & A. Kilicman, 2013. "Fourier Operational Matrices of Differentiation and Transmission: Introduction and Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. F. Toutounian & Emran Tohidi & A. Kilicman, 2013. "Fourier Operational Matrices of Differentiation and Transmission: Introduction and Applications," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, April.
    4. Emran Tohidi & F. Soleymani & Adem Kilicman, 2013. "Robustness of Operational Matrices of Differentiation for Solving State‐Space Analysis and Optimal Control Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. Emran Tohidi & F. Soleymani & Adem Kilicman, 2013. "Robustness of Operational Matrices of Differentiation for Solving State-Space Analysis and Optimal Control Problems," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, April.
    6. 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.
    7. 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).
    8. 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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