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Modified α‐Parameterized Differential Transform Method for Solving Nonlinear Generalized Gardner Equation

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  • Abdulghafor M. Al-Rozbayani
  • Ahmed Farooq Qasim

Abstract

In this article, we present a novel enhancement to the α‐parameterized differential transform method (PDTM) for solving nonlinear boundary value problems. The proposed method is applied to solve the generalized Gardner equation by utilizing genetic algorithms to obtain optimal parameter values. Our proposed approach extends the general differential transformation method, allowing for the use of various values for the coefficient α. Our solution procedure offers a distinct advantage by allowing the original differential transformation method to be divided into multiple steps, thereby illustrating specific solution properties for nonlinear boundary value problems. Additionally, possible alternative solutions based on varying parameter values are also explored and discussed. The results with those obtained through the DTM method and exact solutions are compared to confirm the accuracy of our method and its efficiency in reaching the exact solution quickly.

Suggested Citation

  • Abdulghafor M. Al-Rozbayani & Ahmed Farooq Qasim, 2023. "Modified α‐Parameterized Differential Transform Method for Solving Nonlinear Generalized Gardner Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2023(1).
    • Handle: RePEc:wly:jnljam:v:2023:y:2023:i:1:n:3339655
    DOI: 10.1155/2023/3339655
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    References listed on IDEAS

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    1. Ahmed Farooq Qasim & Ekhlass S. AL-Rawi, 2018. "Adomian Decomposition Method with Modified Bernstein Polynomials for Solving Ordinary and Partial Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2018(1).
    2. Ahmed Farooq Qasim & Ekhlass S. AL-Rawi, 2018. "Adomian Decomposition Method with Modified Bernstein Polynomials for Solving Ordinary and Partial Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2018, pages 1-9, October.
    3. Seyyedeh Roodabeh Moosavi Noori & Nasir Taghizadeh, 2021. "Study of Convergence of Reduced Differential Transform Method for Different Classes of Differential Equations," International Journal of Differential Equations, Hindawi, vol. 2021, pages 1-16, April.
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