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2025, Volume 10, Issue 1: 1367-1383. doi: 10.3934/math.2025063
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High-order numerical method for the fractional Korteweg-de Vries equation using the discontinuous Galerkin method

  • Department of Public Education, Zhengzhou University of Economics and Business, Zhengzhou 450000, China
  • Received: 22 November 2024 Revised: 29 December 2024 Accepted: 14 January 2025 Published: 21 January 2025

  • MSC : 35S10, 65M06, 65M12

  • The fractional Korteweg-de Vries (KdV) equation generalizes the classical KdV equation by incorporating truncation effects within bounded domains, offering a flexible framework for modeling complex phenomena. This paper develops a high-order, fully discrete local discontinuous Galerkin (LDG) method with generalized alternating numerical fluxes to solve the fractional KdV equation, enhancing applicability beyond the limitations of purely alternating fluxes. An efficient finite difference scheme approximates the fractional derivatives, followed by the LDG method for solving the equation. The scheme is proven unconditionally stable and convergent. Numerical experiments confirm the method's accuracy, efficiency, and robustness, highlighting its potential for broader applications in fractional differential equations.

    Citation: Yanhua Gu. High-order numerical method for the fractional Korteweg-de Vries equation using the discontinuous Galerkin method[J]. AIMS Mathematics, 2025, 10(1): 1367-1383. doi: 10.3934/math.2025063

    Related Papers:

  • The fractional Korteweg-de Vries (KdV) equation generalizes the classical KdV equation by incorporating truncation effects within bounded domains, offering a flexible framework for modeling complex phenomena. This paper develops a high-order, fully discrete local discontinuous Galerkin (LDG) method with generalized alternating numerical fluxes to solve the fractional KdV equation, enhancing applicability beyond the limitations of purely alternating fluxes. An efficient finite difference scheme approximates the fractional derivatives, followed by the LDG method for solving the equation. The scheme is proven unconditionally stable and convergent. Numerical experiments confirm the method's accuracy, efficiency, and robustness, highlighting its potential for broader applications in fractional differential equations.



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