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Double Sumudu Transform Iterative Method for One‐Dimensional Nonlinear Coupled Sine‐Gordon Equation

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  • Alemayehu Tamirie Deresse

Abstract

In this paper, the combined double Sumudu transform with iterative method is successfully implemented to obtain the approximate analytical solution of the one‐dimensional coupled nonlinear sine‐Gordon equation (NLSGE) subject to the appropriate initial and boundary conditions which cannot be solved by applying double Sumudu transform only. The solution of the nonlinear part of this equation was solved by a successive iterative method, the proposed technique has the advantage of producing an exact solution, and it is easily applied to the given problems analytically. Two test problems from mathematical physics were taken to show the liability, accuracy, convergence, and efficiency of the proposed method. Furthermore, the results indicate that the introduced method is promising for solving other types of systems of NLPDEs.

Suggested Citation

  • Alemayehu Tamirie Deresse, 2022. "Double Sumudu Transform Iterative Method for One‐Dimensional Nonlinear Coupled Sine‐Gordon Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jnlamp:v:2022:y:2022:i:1:n:6977692
    DOI: 10.1155/2022/6977692
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    References listed on IDEAS

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    1. Yun-Mei Zhao, 2014. "New Exact Solutions for a Higher-Order Wave Equation of KdV Type Using the Multiple Simplest Equation Method," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-13, June.
    2. Yun-Mei Zhao, 2014. "New Exact Solutions for a Higher‐Order Wave Equation of KdV Type Using the Multiple Simplest Equation Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    3. Shams A. Ahmed & Tarig M. Elzaki & Abdelgabar Adam Hassan, 2020. "Solution of Integral Differential Equations by New Double Integral Transform (Laplace–Sumudu Transform)," Abstract and Applied Analysis, Hindawi, vol. 2020, pages 1-7, October.
    4. Yun-Mei Zhao, 2014. "Exact Solutions of Coupled Sine‐Gordon Equations Using the Simplest Equation Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    5. Subashini Vilu & Rokiah Rozita Ahmad & Ummul Khair Salma Din, 2019. "Variational Iteration Method and Sumudu Transform for Solving Delay Differential Equation," International Journal of Differential Equations, Hindawi, vol. 2019, pages 1-6, May.
    6. Shams A. Ahmed & Tarig M. Elzaki & Abdelgabar Adam Hassan, 2020. "Solution of Integral Differential Equations by New Double Integral Transform (Laplace–Sumudu Transform)," Abstract and Applied Analysis, John Wiley & Sons, vol. 2020(1).
    7. Yun-Mei Zhao, 2014. "Exact Solutions of Coupled Sine-Gordon Equations Using the Simplest Equation Method," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-5, February.
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    Cited by:

    1. 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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