Linear Sixth-Order Conservation Difference Scheme for KdV Equation
A numerical investigation is conducted for the initial boundary value problem of the Korteweg–de Vries (KdV) equation with homogeneous boundary conditions. Using the average implicit difference discretization, a second-order theoretical accuracy in time is achieved. For the spatial direction, a cent...
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2025-03-01
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| author | Jie He Jinsong Hu Zhong Chen |
| author_facet | Jie He Jinsong Hu Zhong Chen |
| author_sort | Jie He |
| collection | DOAJ |
| description | A numerical investigation is conducted for the initial boundary value problem of the Korteweg–de Vries (KdV) equation with homogeneous boundary conditions. Using the average implicit difference discretization, a second-order theoretical accuracy in time is achieved. For the spatial direction, a center-symmetric discretization coupled with the extrapolation technique is employed, yielding a three-level linear difference method with sixth-order accuracy. Consequently, the integration of these methods results in a linear finite difference scheme that accurately simulates the two conserved quantities of the original problem. Furthermore, theoretical results, including the convergence and stability of the proposed scheme, are proved using the discrete Sobolev inequality and the discrete Gronwall inequality. Numerical experiments validate the reliability of the scheme. |
| format | Article |
| id | doaj-art-c1af04f147304e12bb862df13574e56f |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-03-01 |
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| series | Mathematics |
| spelling | doaj-art-c1af04f147304e12bb862df13574e56f2025-08-20T03:06:20ZengMDPI AGMathematics2227-73902025-03-01137113210.3390/math13071132Linear Sixth-Order Conservation Difference Scheme for KdV EquationJie He0Jinsong Hu1Zhong Chen2College of Big Data and Artificial Intelligence, Chengdu Technological University, Chengdu 611730, ChinaCollege of Big Data and Artificial Intelligence, Chengdu Technological University, Chengdu 611730, ChinaApplied Nuclear Technology in Geosciences Key Laboratory of Sichuan, Chengdu University of Technology, Chengdu 610059, ChinaA numerical investigation is conducted for the initial boundary value problem of the Korteweg–de Vries (KdV) equation with homogeneous boundary conditions. Using the average implicit difference discretization, a second-order theoretical accuracy in time is achieved. For the spatial direction, a center-symmetric discretization coupled with the extrapolation technique is employed, yielding a three-level linear difference method with sixth-order accuracy. Consequently, the integration of these methods results in a linear finite difference scheme that accurately simulates the two conserved quantities of the original problem. Furthermore, theoretical results, including the convergence and stability of the proposed scheme, are proved using the discrete Sobolev inequality and the discrete Gronwall inequality. Numerical experiments validate the reliability of the scheme.https://www.mdpi.com/2227-7390/13/7/1132KdV equationthree levelhigh accuracyconservationconvergencestability |
| spellingShingle | Jie He Jinsong Hu Zhong Chen Linear Sixth-Order Conservation Difference Scheme for KdV Equation Mathematics KdV equation three level high accuracy conservation convergence stability |
| title | Linear Sixth-Order Conservation Difference Scheme for KdV Equation |
| title_full | Linear Sixth-Order Conservation Difference Scheme for KdV Equation |
| title_fullStr | Linear Sixth-Order Conservation Difference Scheme for KdV Equation |
| title_full_unstemmed | Linear Sixth-Order Conservation Difference Scheme for KdV Equation |
| title_short | Linear Sixth-Order Conservation Difference Scheme for KdV Equation |
| title_sort | linear sixth order conservation difference scheme for kdv equation |
| topic | KdV equation three level high accuracy conservation convergence stability |
| url | https://www.mdpi.com/2227-7390/13/7/1132 |
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