High-order numerical method for the fractional Korteweg-de Vries equation using the discontinuous Galerkin method
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...
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AIMS Press
2025-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025063 |
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| author | Yanhua Gu |
| author_facet | Yanhua Gu |
| author_sort | Yanhua Gu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-3a169a339c624b26a9269b300ff8a2fc |
| institution | DOAJ |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-3a169a339c624b26a9269b300ff8a2fc2025-08-20T02:48:13ZengAIMS PressAIMS Mathematics2473-69882025-01-011011367138310.3934/math.2025063High-order numerical method for the fractional Korteweg-de Vries equation using the discontinuous Galerkin methodYanhua Gu0Department of Public Education, Zhengzhou University of Economics and Business, Zhengzhou 450000, ChinaThe 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.https://www.aimspress.com/article/doi/10.3934/math.2025063fractional derivativefinite element methodstabilityerror analysis |
| spellingShingle | Yanhua Gu High-order numerical method for the fractional Korteweg-de Vries equation using the discontinuous Galerkin method AIMS Mathematics fractional derivative finite element method stability error analysis |
| title | High-order numerical method for the fractional Korteweg-de Vries equation using the discontinuous Galerkin method |
| title_full | High-order numerical method for the fractional Korteweg-de Vries equation using the discontinuous Galerkin method |
| title_fullStr | High-order numerical method for the fractional Korteweg-de Vries equation using the discontinuous Galerkin method |
| title_full_unstemmed | High-order numerical method for the fractional Korteweg-de Vries equation using the discontinuous Galerkin method |
| title_short | High-order numerical method for the fractional Korteweg-de Vries equation using the discontinuous Galerkin method |
| title_sort | high order numerical method for the fractional korteweg de vries equation using the discontinuous galerkin method |
| topic | fractional derivative finite element method stability error analysis |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025063 |
| work_keys_str_mv | AT yanhuagu highordernumericalmethodforthefractionalkortewegdevriesequationusingthediscontinuousgalerkinmethod |