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A Higher-Order Approach For Time-Fractional Generalized Burgers’ Equation

Author

Listed:
  • KOMAL TANEJA

    (Department of Mathematics, Birla Institute of Technology and Science, Pilani, Rajasthan 333031, India)

  • KOMAL DESWAL

    (Department of Mathematics, Birla Institute of Technology and Science, Pilani, Rajasthan 333031, India)

  • DEVENDRA KUMAR

    (Department of Mathematics, Birla Institute of Technology and Science, Pilani, Rajasthan 333031, India)

  • DUMITRU BALEANU

    (Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankaya University, TR-06530 Ankara, Turkey3Institute of Space Science, R-077125 Magurle-Bucharest, Romania)

Abstract

A fast higher-order scheme is established for solving inhomogeneous time-fractional generalized Burgers’ equation. The time-fractional operator is taken as the modified operator with the Mittag-Leffler kernel. Through stability analysis, it has been demonstrated that the proposed numerical approach is unconditionally stable. The convergence of the numerical method is analyzed theoretically using von Neumann’s method. It has been proved that the proposed numerical method is fourth-order convergent in space and second-order convergent in time in the L2-norm. The scheme’s proficiency and effectiveness are examined through two numerical experiments to validate the theoretical estimates. The tabular and graphical representations of numerical results confirm the high accuracy and versatility of the scheme.

Suggested Citation

  • Komal Taneja & Komal Deswal & Devendra Kumar & Dumitru Baleanu, 2023. "A Higher-Order Approach For Time-Fractional Generalized Burgers’ Equation," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(07), pages 1-22.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:07:n:s0218348x23500676
    DOI: 10.1142/S0218348X23500676
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