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Solutions of Two‐Dimensional Nonlinear Sine‐Gordon Equation via Triple Laplace Transform Coupled with Iterative Method

Author

Listed:
  • Alemayehu Tamirie Deresse
  • Yesuf Obsie Mussa
  • Ademe Kebede Gizaw

Abstract

This article presents triple Laplace transform coupled with iterative method to obtain the exact solution of two‐dimensional nonlinear sine‐Gordon equation (NLSGE) subject to the appropriate initial and boundary conditions. The noise term in this equation is vanished by successive iterative method. The proposed technique has the advantage of producing exact solution, and it is easily applied to the given problems analytically. Four test problems from mathematical physics are taken to show the accuracy, convergence, and the efficiency of the proposed method. Furthermore, the results indicate that the introduced method is promising for solving other type systems of NLPDEs.

Suggested Citation

  • Alemayehu Tamirie Deresse & Yesuf Obsie Mussa & Ademe Kebede Gizaw, 2021. "Solutions of Two‐Dimensional Nonlinear Sine‐Gordon Equation via Triple Laplace Transform Coupled with Iterative Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2021(1).
    • Handle: RePEc:wly:jnljam:v:2021:y:2021:i:1:n:9279022
    DOI: 10.1155/2021/9279022
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    References listed on IDEAS

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    1. Sachin Bhalekar & Varsha Daftardar-Gejji, 2011. "Convergence of the New Iterative Method," International Journal of Differential Equations, Hindawi, vol. 2011, pages 1-10, November.
    2. Abdon Atangana, 2013. "A Note on the Triple Laplace Transform and Its Applications to Some Kind of Third-Order Differential Equation," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, June.
    3. Hassan Eltayeb & Adem Kiliçman, 2013. "A Note on Double Laplace Transform and Telegraphic Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Abdon Atangana, 2013. "A Note on the Triple Laplace Transform and Its Applications to Some Kind of Third‐Order Differential Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. Hassan Eltayeb & Adem Kiliçman, 2013. "A Note on Double Laplace Transform and Telegraphic Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-6, February.
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    Cited by:

    1. Alemayehu Tamirie Deresse, 2022. "Analytical Solutions to Two‐Dimensional Nonlinear Telegraph Equations Using the Conformable Triple Laplace Transform Iterative Method," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    2. Asfaw Tsegaye Moltot & Alemayehu Tamirie Deresse, 2022. "Approximate Analytical Solution to Nonlinear Delay Differential Equations by Using Sumudu Iterative Method," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).

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