A Space-Time Legendre-Petrov-Galerkin Method for Third-Order Differential Equations
In this article, a space-time spectral method is considered to approximate third-order differential equations with non-periodic boundary conditions. The Legendre-Petrov-Galerkin discretization is employed in both space and time. In the theoretical analysis, rigorous proof of error estimates in the w...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/3/281 |
| _version_ | 1827751359199313920 |
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| author | Siqin Tang Hong Li |
| author_facet | Siqin Tang Hong Li |
| author_sort | Siqin Tang |
| collection | DOAJ |
| description | In this article, a space-time spectral method is considered to approximate third-order differential equations with non-periodic boundary conditions. The Legendre-Petrov-Galerkin discretization is employed in both space and time. In the theoretical analysis, rigorous proof of error estimates in the weighted space-time norms is obtained for the fully discrete scheme. We also formulate the matrix form of the fully discrete scheme by taking appropriate test and trial functions in both space and time. Finally, extensive numerical experiments are conducted for linear and nonlinear problems, and spectral accuracy is derived for both space and time. Moreover, the numerical results are compared with those computed by other numerical methods to confirm the efficiency of the proposed method. |
| first_indexed | 2024-03-11T06:57:02Z |
| format | Article |
| id | doaj.art-fcba27778bd94ae88754ace2cdcb8357 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T06:57:02Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-fcba27778bd94ae88754ace2cdcb83572023-11-17T09:35:19ZengMDPI AGAxioms2075-16802023-03-0112328110.3390/axioms12030281A Space-Time Legendre-Petrov-Galerkin Method for Third-Order Differential EquationsSiqin Tang0Hong Li1Faculty of Science, Inner Mongolia University of Technology, Hohhot 010021, ChinaSchool of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, ChinaIn this article, a space-time spectral method is considered to approximate third-order differential equations with non-periodic boundary conditions. The Legendre-Petrov-Galerkin discretization is employed in both space and time. In the theoretical analysis, rigorous proof of error estimates in the weighted space-time norms is obtained for the fully discrete scheme. We also formulate the matrix form of the fully discrete scheme by taking appropriate test and trial functions in both space and time. Finally, extensive numerical experiments are conducted for linear and nonlinear problems, and spectral accuracy is derived for both space and time. Moreover, the numerical results are compared with those computed by other numerical methods to confirm the efficiency of the proposed method.https://www.mdpi.com/2075-1680/12/3/281third-order differential equationsLegendre-Petrov-Galerkin methodsspace-time spectral methodsexponential convergence |
| spellingShingle | Siqin Tang Hong Li A Space-Time Legendre-Petrov-Galerkin Method for Third-Order Differential Equations Axioms third-order differential equations Legendre-Petrov-Galerkin methods space-time spectral methods exponential convergence |
| title | A Space-Time Legendre-Petrov-Galerkin Method for Third-Order Differential Equations |
| title_full | A Space-Time Legendre-Petrov-Galerkin Method for Third-Order Differential Equations |
| title_fullStr | A Space-Time Legendre-Petrov-Galerkin Method for Third-Order Differential Equations |
| title_full_unstemmed | A Space-Time Legendre-Petrov-Galerkin Method for Third-Order Differential Equations |
| title_short | A Space-Time Legendre-Petrov-Galerkin Method for Third-Order Differential Equations |
| title_sort | space time legendre petrov galerkin method for third order differential equations |
| topic | third-order differential equations Legendre-Petrov-Galerkin methods space-time spectral methods exponential convergence |
| url | https://www.mdpi.com/2075-1680/12/3/281 |
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