{"title":"一类拟变量网格高分辨率紧凑算子格式的Burger - huxley和Burger - fisher方程","authors":"Navnit Jha, Madhav Wagley","doi":"10.5206/mase/10837","DOIUrl":null,"url":null,"abstract":"We describe a quasi-variable meshes implicit compact finite-difference discretization having an accuracy of order four in the spatial direction and second-order in the temporal direction for obtaining numerical solution values of generalized Burger’s-Huxley and Burger’s-Fisher equations. The new difference scheme is derived for a general one-dimension quasi-linear parabolic partial differential equation on a quasi-variable meshes network to the extent that the magnitude of local truncation error of the high-order compact scheme remains unchanged in case of uniform meshes network. Practically, quasi-variable meshes high-order compact schemes yield more precise solution compared with uniform meshes high-order schemes of the same magnitude. A detailed exposition of the new scheme has been introduced and discussed the Fourier analysis based stability theory. The computational results with generalized Burger’s-Huxley equation and Burger’s-Fisher equation are obtained using quasi-variable meshes high-order compact scheme and compared with a numerical solution using uniform meshes high-order schemes to demonstrate capability and accuracy.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2020-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A family of quasi-variable meshes high-resolution compact operator scheme for Burger's-Huxley, and Burger's-Fisher equation\",\"authors\":\"Navnit Jha, Madhav Wagley\",\"doi\":\"10.5206/mase/10837\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We describe a quasi-variable meshes implicit compact finite-difference discretization having an accuracy of order four in the spatial direction and second-order in the temporal direction for obtaining numerical solution values of generalized Burger’s-Huxley and Burger’s-Fisher equations. The new difference scheme is derived for a general one-dimension quasi-linear parabolic partial differential equation on a quasi-variable meshes network to the extent that the magnitude of local truncation error of the high-order compact scheme remains unchanged in case of uniform meshes network. Practically, quasi-variable meshes high-order compact schemes yield more precise solution compared with uniform meshes high-order schemes of the same magnitude. A detailed exposition of the new scheme has been introduced and discussed the Fourier analysis based stability theory. The computational results with generalized Burger’s-Huxley equation and Burger’s-Fisher equation are obtained using quasi-variable meshes high-order compact scheme and compared with a numerical solution using uniform meshes high-order schemes to demonstrate capability and accuracy.\",\"PeriodicalId\":93797,\"journal\":{\"name\":\"Mathematics in applied sciences and engineering\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2020-11-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics in applied sciences and engineering\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5206/mase/10837\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics in applied sciences and engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5206/mase/10837","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
A family of quasi-variable meshes high-resolution compact operator scheme for Burger's-Huxley, and Burger's-Fisher equation
We describe a quasi-variable meshes implicit compact finite-difference discretization having an accuracy of order four in the spatial direction and second-order in the temporal direction for obtaining numerical solution values of generalized Burger’s-Huxley and Burger’s-Fisher equations. The new difference scheme is derived for a general one-dimension quasi-linear parabolic partial differential equation on a quasi-variable meshes network to the extent that the magnitude of local truncation error of the high-order compact scheme remains unchanged in case of uniform meshes network. Practically, quasi-variable meshes high-order compact schemes yield more precise solution compared with uniform meshes high-order schemes of the same magnitude. A detailed exposition of the new scheme has been introduced and discussed the Fourier analysis based stability theory. The computational results with generalized Burger’s-Huxley equation and Burger’s-Fisher equation are obtained using quasi-variable meshes high-order compact scheme and compared with a numerical solution using uniform meshes high-order schemes to demonstrate capability and accuracy.