Stability analysis and convergence rate of a two-step predictor-corrector approach for shallow water equations with source terms
This paper deals with a two-step explicit predictor-corrector approach so-called the two-step MacCormack formulation, for solving the one-dimensional nonlinear shallow water equations with source terms. The proposed two-step numerical scheme uses the fractional steps procedure to treat the friction...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023465?viewType=HTML |
| _version_ | 1811160954126204928 |
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| author | Rubayyi T. Alqahtani Jean C. Ntonga Eric Ngondiep |
| author_facet | Rubayyi T. Alqahtani Jean C. Ntonga Eric Ngondiep |
| author_sort | Rubayyi T. Alqahtani |
| collection | DOAJ |
| description | This paper deals with a two-step explicit predictor-corrector approach so-called the two-step MacCormack formulation, for solving the one-dimensional nonlinear shallow water equations with source terms. The proposed two-step numerical scheme uses the fractional steps procedure to treat the friction slope and to upwind the convection term in order to control the numerical oscillations and stability. The developed scheme uses both forward and backward difference formulations in the predictor and corrector steps, respectively. The linear stability of the constructed technique is deeply analyzed using the Von Neumann stability approach whereas the convergence rate of the proposed method is numerically obtained in the $ L^{2} $-norm. A wide set of numerical examples confirm the theoretical results. |
| first_indexed | 2024-04-10T06:06:26Z |
| format | Article |
| id | doaj.art-a618f1955bb441249c16f580de0463f4 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-10T06:06:26Z |
| publishDate | 2023-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-a618f1955bb441249c16f580de0463f42023-03-03T01:19:47ZengAIMS PressAIMS Mathematics2473-69882023-02-01849265928910.3934/math.2023465Stability analysis and convergence rate of a two-step predictor-corrector approach for shallow water equations with source termsRubayyi T. Alqahtani 0 Jean C. Ntonga1Eric Ngondiep2 1. Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), 90950 Riyadh 11632, Saudi Arabia2. Hydrological Research Centre, Institute for Geological and Mining Research, 4110 Yaounde-Cameroon1. Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), 90950 Riyadh 11632, Saudi Arabia 2. Hydrological Research Centre, Institute for Geological and Mining Research, 4110 Yaounde-CameroonThis paper deals with a two-step explicit predictor-corrector approach so-called the two-step MacCormack formulation, for solving the one-dimensional nonlinear shallow water equations with source terms. The proposed two-step numerical scheme uses the fractional steps procedure to treat the friction slope and to upwind the convection term in order to control the numerical oscillations and stability. The developed scheme uses both forward and backward difference formulations in the predictor and corrector steps, respectively. The linear stability of the constructed technique is deeply analyzed using the Von Neumann stability approach whereas the convergence rate of the proposed method is numerically obtained in the $ L^{2} $-norm. A wide set of numerical examples confirm the theoretical results.https://www.aimspress.com/article/doi/10.3934/math.2023465?viewType=HTMLshallow water equationssource termsa two-step explicit predictor-corrector approachfourier stability analysislinear stability conditionconvergence rate |
| spellingShingle | Rubayyi T. Alqahtani Jean C. Ntonga Eric Ngondiep Stability analysis and convergence rate of a two-step predictor-corrector approach for shallow water equations with source terms AIMS Mathematics shallow water equations source terms a two-step explicit predictor-corrector approach fourier stability analysis linear stability condition convergence rate |
| title | Stability analysis and convergence rate of a two-step predictor-corrector approach for shallow water equations with source terms |
| title_full | Stability analysis and convergence rate of a two-step predictor-corrector approach for shallow water equations with source terms |
| title_fullStr | Stability analysis and convergence rate of a two-step predictor-corrector approach for shallow water equations with source terms |
| title_full_unstemmed | Stability analysis and convergence rate of a two-step predictor-corrector approach for shallow water equations with source terms |
| title_short | Stability analysis and convergence rate of a two-step predictor-corrector approach for shallow water equations with source terms |
| title_sort | stability analysis and convergence rate of a two step predictor corrector approach for shallow water equations with source terms |
| topic | shallow water equations source terms a two-step explicit predictor-corrector approach fourier stability analysis linear stability condition convergence rate |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023465?viewType=HTML |
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