{"title":"BBM方程的一种新的多辛欧拉盒格式","authors":"Haochen Li , Jianqiang Sun","doi":"10.1016/j.mcm.2013.06.012","DOIUrl":null,"url":null,"abstract":"<div><p>A new scheme for the BBM equation with the accuracy order of <span><math><mi>O</mi><mrow><mo>(</mo><mo>△</mo><msup><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mo>△</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></math></span> is proposed. The multi-symplectic conservation property of the new scheme is proved. The backward error analysis of the new scheme is implemented. The solitary wave evolution behaviors are simulated by the new scheme. The new multi-symplectic Euler box scheme is compared with the classical Euler box scheme and the Preissman box scheme in preserving the conservation properties of the BBM equation and the computation cost.</p></div>","PeriodicalId":49872,"journal":{"name":"Mathematical and Computer Modelling","volume":"58 7","pages":"Pages 1489-1501"},"PeriodicalIF":0.0000,"publicationDate":"2013-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.mcm.2013.06.012","citationCount":"10","resultStr":"{\"title\":\"A new multi-symplectic Euler box scheme for the BBM equation\",\"authors\":\"Haochen Li , Jianqiang Sun\",\"doi\":\"10.1016/j.mcm.2013.06.012\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>A new scheme for the BBM equation with the accuracy order of <span><math><mi>O</mi><mrow><mo>(</mo><mo>△</mo><msup><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mo>△</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></math></span> is proposed. The multi-symplectic conservation property of the new scheme is proved. The backward error analysis of the new scheme is implemented. The solitary wave evolution behaviors are simulated by the new scheme. The new multi-symplectic Euler box scheme is compared with the classical Euler box scheme and the Preissman box scheme in preserving the conservation properties of the BBM equation and the computation cost.</p></div>\",\"PeriodicalId\":49872,\"journal\":{\"name\":\"Mathematical and Computer Modelling\",\"volume\":\"58 7\",\"pages\":\"Pages 1489-1501\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.mcm.2013.06.012\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical and Computer Modelling\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0895717713002355\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical and Computer Modelling","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0895717713002355","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A new multi-symplectic Euler box scheme for the BBM equation
A new scheme for the BBM equation with the accuracy order of is proposed. The multi-symplectic conservation property of the new scheme is proved. The backward error analysis of the new scheme is implemented. The solitary wave evolution behaviors are simulated by the new scheme. The new multi-symplectic Euler box scheme is compared with the classical Euler box scheme and the Preissman box scheme in preserving the conservation properties of the BBM equation and the computation cost.
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