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Solution of the Differential‐Difference Equations by Optimal Homotopy Asymptotic Method

Author

Listed:
  • H. Ullah
  • S. Islam
  • M. Idrees
  • M. Fiza

Abstract

We applied a new analytic approximate technique, optimal homotopy asymptotic method (OHAM), for treatment of differential‐difference equations (DDEs). To see the efficiency and reliability of the method, we consider Volterra equation in different form. It provides us with a convenient way to control the convergence of approximate solutions when it is compared with other methods of solution found in the literature. The obtained solutions show that OHAM is effective, simpler, easier, and explicit.

Suggested Citation

  • H. Ullah & S. Islam & M. Idrees & M. Fiza, 2014. "Solution of the Differential‐Difference Equations by Optimal Homotopy Asymptotic Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:520467
    DOI: 10.1155/2014/520467
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    References listed on IDEAS

    as
    1. Zhang, Da-jun, 2005. "Singular solutions in Casoratian form for two differential-difference equations," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1333-1350.
    2. Dai, Chaoqing & Zhu, Jiamin & Zhang, Jiefang, 2006. "New exact solutions to the mKdV equation with variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 881-886.
    3. R. Nawaz & H. Ullah & S. Islam & M. Idrees, 2013. "Application of Optimal Homotopy Asymptotic Method to Burger Equations," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-8, July.
    4. R. Nawaz & H. Ullah & S. Islam & M. Idrees, 2013. "Application of Optimal Homotopy Asymptotic Method to Burger Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    5. H. Ullah & S. Islam & M. Idrees & M. Arif, 2013. "Solution of Boundary Layer Problems with Heat Transfer by Optimal Homotopy Asymptotic Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    6. H. Ullah & S. Islam & M. Idrees & R. Nawaz, 2013. "Application of Optimal Homotopy Asymptotic Method to Doubly Wave Solutions of the Coupled Drinfel’d-Sokolov-Wilson Equations," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-8, December.
    7. H. Ullah & S. Islam & M. Idrees & M. Arif, 2013. "Solution of Boundary Layer Problems with Heat Transfer by Optimal Homotopy Asymptotic Method," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, September.
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