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Computational Study of Multiterm Time‐Fractional Differential Equation Using Cubic B‐Spline Finite Element Method

Author

Listed:
  • Shams Ul Arifeen
  • Sirajul Haq
  • Farhan Golkarmanesh

Abstract

Due to the symmetry feature in nature, fractional differential equations precisely measure and describe biological and physical processes. Multiterm time‐fractional order has been introduced to model complex processes in different physical phenomena. This article presents a numerical method based on the cubic B‐spline finite element method for the solution of multiterm time‐fractional differential equations. The temporal fractional part is defined in the Caputo sense while the B‐spline finite element method is employed for space approximation. In addition, the four‐point Gauss−Legendre quadrature is applied to evaluate the source term. The stability of the proposed scheme is discussed by the Von Neumann method, which verifies that the scheme is unconditionally stable. L2 and L∞ norms are used to check the efficiency and accuracy of the proposed scheme. Computed results are compared with the exact and available methods in the literature, which show the betterment of the proposed method.

Suggested Citation

  • Shams Ul Arifeen & Sirajul Haq & Farhan Golkarmanesh, 2022. "Computational Study of Multiterm Time‐Fractional Differential Equation Using Cubic B‐Spline Finite Element Method," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:3160725
    DOI: 10.1155/2022/3160725
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    References listed on IDEAS

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    1. Gupta, A.K. & Ray, S. Saha, 2018. "On the solution of time-fractional KdV–Burgers equation using Petrov–Galerkin method for propagation of long wave in shallow water," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 376-380.
    2. Xiaozhong Yang & Lifei Wu, 2020. "A New Kind of Parallel Natural Difference Method for Multi-Term Time Fractional Diffusion Model," Mathematics, MDPI, vol. 8(4), pages 1-19, April.
    3. Vasily E. Tarasov, 2020. "Mathematical Economics: Application of Fractional Calculus," Mathematics, MDPI, vol. 8(5), pages 1-3, April.
    4. Shams Ul Arifeen & Sirajul Haq & Farhan Golkarmanesh & Jesus M. Munoz-Pacheco, 2022. "Computational Study of Multiterm Time-Fractional Differential Equation Using Cubic B-Spline Finite Element Method," Complexity, Hindawi, vol. 2022, pages 1-15, November.
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    Cited by:

    1. Jing Zhu & Zhe Yin, 2025. "A B-spline Finite Element Method for Structural Damping Beam Vibration Problem," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 17(5), pages 1-10, December.

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