{"title":"带源项的浅水方程两步预测校正方法的稳定性分析和收敛速度","authors":"R. T. Alqahtani, J. Ntonga, E. Ngondiep","doi":"10.3934/math.2023465","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Stability analysis and convergence rate of a two-step predictor-corrector approach for shallow water equations with source terms\",\"authors\":\"R. T. Alqahtani, J. Ntonga, E. Ngondiep\",\"doi\":\"10.3934/math.2023465\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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.\",\"PeriodicalId\":48562,\"journal\":{\"name\":\"AIMS Mathematics\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"AIMS Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3934/math.2023465\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"AIMS Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/math.2023465","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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 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.
期刊介绍:
AIMS Mathematics is an international Open Access journal devoted to publishing peer-reviewed, high quality, original papers in all fields of mathematics. We publish the following article types: original research articles, reviews, editorials, letters, and conference reports.