Kyungpook Mathematical Journal

  • 제60권4호
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  • Pages.753-765
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  • 2020
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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The Multi-step Adomian Decomposition Method for Approximating a Fractional Smoking Habit Model

  • Zuriqat, Mohammad (Department of Mathematics, Al al-Bayt University) ;
  • Freihat, Asad (Department of Applied Science, Ajloun College, Al-Balqa Applied University)
  • 투고 : 2015.06.10
  • 심사 : 2019.06.21
  • 발행 : 2020.12.31
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초록

Smoking is one of the main causes of health problems and continues to be one of the world's most significant health challenges. In this paper, we use the multi-step Adomian decomposition method (MSADM) to obtain approximate analytical solutions for a mathematical fractional model of the evolution of the smoking habit. The proposed MSADM scheme is only a simple modification of the Adomian decomposition method (ADM), in which ADM is treated algorithmically with a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding problems. A comparative study between the new algorithm and the classical Runge-Kutta method is presented in the case of integer-order derivatives. The solutions obtained are also presented graphically. The results reveal that the method is effective and convenient for solving linear and nonlinear differential equations of fractional order.

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