{"title":"基于Volterra级数的Burgers方程解析解的评价","authors":"M. Schiffner, M. Mleczko, G. Schmitz","doi":"10.1109/ULTSYM.2009.5442057","DOIUrl":null,"url":null,"abstract":"A simple, well-interpretable, and explicit analytical solution to the Burgers equation based on Volterra series is derived. Its region of convergence is investigated and a method for the computationally efficient numerical evaluation of the associated Volterra polynomials is presented. For a given boundary condition, numerical results are compared to a widely-used numerical standard solution. After a propagation distance of 10 cm in steps of 5 mm the Volterra polynomials of degree 2 and 3 achieve relative errors in terms of the L2-norm of 4.22% and 1.35%, respectively.","PeriodicalId":368182,"journal":{"name":"2009 IEEE International Ultrasonics Symposium","volume":"42 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2009-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Evaluation of an analytical solution to the Burgers equation based on Volterra series\",\"authors\":\"M. Schiffner, M. Mleczko, G. Schmitz\",\"doi\":\"10.1109/ULTSYM.2009.5442057\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A simple, well-interpretable, and explicit analytical solution to the Burgers equation based on Volterra series is derived. Its region of convergence is investigated and a method for the computationally efficient numerical evaluation of the associated Volterra polynomials is presented. For a given boundary condition, numerical results are compared to a widely-used numerical standard solution. After a propagation distance of 10 cm in steps of 5 mm the Volterra polynomials of degree 2 and 3 achieve relative errors in terms of the L2-norm of 4.22% and 1.35%, respectively.\",\"PeriodicalId\":368182,\"journal\":{\"name\":\"2009 IEEE International Ultrasonics Symposium\",\"volume\":\"42 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2009-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2009 IEEE International Ultrasonics Symposium\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ULTSYM.2009.5442057\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2009 IEEE International Ultrasonics Symposium","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ULTSYM.2009.5442057","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Evaluation of an analytical solution to the Burgers equation based on Volterra series
A simple, well-interpretable, and explicit analytical solution to the Burgers equation based on Volterra series is derived. Its region of convergence is investigated and a method for the computationally efficient numerical evaluation of the associated Volterra polynomials is presented. For a given boundary condition, numerical results are compared to a widely-used numerical standard solution. After a propagation distance of 10 cm in steps of 5 mm the Volterra polynomials of degree 2 and 3 achieve relative errors in terms of the L2-norm of 4.22% and 1.35%, respectively.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
