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(n+1)-Dimensional reduced differential transform method for solving partial differential equations

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  • Yu, Jianping
  • Jing, Jian
  • Sun, Yongli
  • Wu, Suping

Abstract

In this paper, we study the generalization of the reduced differential transform method to (n+1)-dimensional case, thus, the partial differential equations (PDEs) can be solved efficiently. One distinctive practical feature of this method is that it is applied without using discretization, or restrictive assumptions, the other is that large computational work and round-off errors are avoided. We employ the proposed method on a few initial value problems to illustrate it is highly accurate and more efficient. Hence, our method is a powerful method for solving the PDEs and problems arising in physics, engineering area, and so on.

Suggested Citation

  • Yu, Jianping & Jing, Jian & Sun, Yongli & Wu, Suping, 2016. "(n+1)-Dimensional reduced differential transform method for solving partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 697-705.
    • Handle: RePEc:eee:apmaco:v:273:y:2016:i:c:p:697-705
    DOI: 10.1016/j.amc.2015.10.016
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    References listed on IDEAS

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    1. Arikoglu, Aytac & Ozkol, Ibrahim, 2007. "Solution of fractional differential equations by using differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1473-1481.
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    2. Bo Ren & Ji Lin & Zhi-Mei Lou, 2019. "A New Nonlinear Equation with Lump-Soliton, Lump-Periodic, and Lump-Periodic-Soliton Solutions," Complexity, Hindawi, vol. 2019, pages 1-10, June.
    3. Salah Abuasad & Ahmet Yildirim & Ishak Hashim & Samsul Ariffin Abdul Karim & J.F. Gómez-Aguilar, 2019. "Fractional Multi-Step Differential Transformed Method for Approximating a Fractional Stochastic SIS Epidemic Model with Imperfect Vaccination," IJERPH, MDPI, vol. 16(6), pages 1-15, March.
    4. Liu, Ling & Wen, Xiao-Yong & Liu, Nan & Jiang, Tao & Yuan, Jin-Yun, 2020. "An integrable lattice hierarchy associated with a 4 × 4 matrix spectral problem: N-fold Darboux transformation and dynamical properties," Applied Mathematics and Computation, Elsevier, vol. 387(C).

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