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Approximate Analytical Solution to Nonlinear Delay Differential Equations by Using Sumudu Iterative Method

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  • Asfaw Tsegaye Moltot
  • Alemayehu Tamirie Deresse

Abstract

In this study, an efficient analytical method called the Sumudu Iterative Method (SIM) is introduced to obtain the solutions for the nonlinear delay differential equation (NDDE). This technique is a mixture of the Sumudu transform method and the new iterative method. The Sumudu transform method is used in this approach to solve the equation’s linear portion, and the new iterative method’s successive iterative producers are used to solve the equation’s nonlinear portion. Some basic properties and theorems which help us to solve the governing problem using the suggested approach are revised. The benefit of this approach is that it solves the equations directly and reliably, without the prerequisite for perturbations or linearization or extensive computer labor. Five sample instances from the DDEs are given to confirm the method’s reliability and effectiveness, and the outcomes are compared with the exact solution with the assistance of tables and graphs after taking the sum of the first eight iterations of the approximate solution. Furthermore, the findings indicate that the recommended strategy is encouraging for solving other types of nonlinear delay differential equations.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlamp:v:2022:y:2022:i:1:n:2466367
    DOI: 10.1155/2022/2466367
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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. Ekhlass S. Al-Rawi & Merna A. Samarchi & Shyam L. Kalla, 2022. "On the Use of Elzaki Decomposition Method for Solving Higher-Order Integro-Differential Equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2022, pages 1-8, February.
    3. Shahram Rezapour & Muhammad Imran Liaqat & Sina Etemad, 2022. "An Effective New Iterative Method to Solve Conformable Cauchy Reaction‐Diffusion Equation via the Shehu Transform," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    4. Alemayehu Tamirie Deresse & Antonio Scarfone, 2022. "Double Sumudu Transform Iterative Method for One-Dimensional Nonlinear Coupled Sine-Gordon Equation," Advances in Mathematical Physics, Hindawi, vol. 2022, pages 1-15, January.
    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. Alemayehu Tamirie Deresse & Andr Nicolet, 2022. "Analytical Solution of One-Dimensional Nonlinear Conformable Fractional Telegraph Equation by Reduced Differential Transform Method," Advances in Mathematical Physics, Hindawi, vol. 2022, pages 1-18, July.
    7. Mamta Kapoor & Nehad Ali Shah & Salman Saleem & Wajaree Weera, 2022. "An Analytical Approach for Fractional Hyperbolic Telegraph Equation Using Shehu Transform in One, Two and Three Dimensions," Mathematics, MDPI, vol. 10(12), pages 1-26, June.
    8. 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).
    9. P. Hammachukiattikul & E. Sekar & A. Tamilselvan & R. Vadivel & N. Gunasekaran & Praveen Agarwal & Xiaolong Qin, 2021. "Comparative Study on Numerical Methods for Singularly Perturbed Advanced-Delay Differential Equations," Journal of Mathematics, Hindawi, vol. 2021, pages 1-15, June.
    10. 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).
    11. 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, Hindawi, vol. 2021, pages 1-15, October.
    12. Alemayehu Tamirie Deresse & Andrei Mironov, 2022. "Analytical Solutions to Two-Dimensional Nonlinear Telegraph Equations Using the Conformable Triple Laplace Transform Iterative Method," Advances in Mathematical Physics, Hindawi, vol. 2022, pages 1-17, June.
    13. Alemayehu Tamirie Deresse, 2022. "Analytical Solution of One‐Dimensional Nonlinear Conformable Fractional Telegraph Equation by Reduced Differential Transform Method," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    14. 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).
    15. Xiankang Luo & Mustafa Habib & Shazia Karim & Hanan A. Wahash, 2022. "Semianalytical Approach for the Approximate Solution of Delay Differential Equations," Complexity, John Wiley & Sons, vol. 2022(1).
    16. Xiankang Luo & Mustafa Habib & Shazia Karim & Hanan A. Wahash & Fathalla A. Rihan, 2022. "Semianalytical Approach for the Approximate Solution of Delay Differential Equations," Complexity, Hindawi, vol. 2022, pages 1-6, June.
    17. Shahram Rezapour & Muhammad Imran Liaqat & Sina Etemad & Kolade M. Owolabi, 2022. "An Effective New Iterative Method to Solve Conformable Cauchy Reaction-Diffusion Equation via the Shehu Transform," Journal of Mathematics, Hindawi, vol. 2022, pages 1-12, June.
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