{"title":"半线性双曲方程近似混合问题的差分电路解系数稳定性","authors":"П. П. Матус, С. В. Лемешевский","doi":"10.29235/1561-8323-2020-64-2-135-143","DOIUrl":null,"url":null,"abstract":"The stability with respect to coefficients of solution of a difference scheme approximating the initial boundary-value problem for the one-dimensional semi-linear hyperbolic equation is studied. The estimates of the solutions of both differential and difference problems are obtained. In the domain of existence of the solution, the estimates for perturbation of the solution of a difference scheme with respect to perturbation of the coefficients of the equation are obtained. These estimates are consistent with the estimates for the differential problem. In all cases, the method of energy inequalities, the Bihari inequality and its mesh analogue are used.","PeriodicalId":11227,"journal":{"name":"Doklady Akademii nauk","volume":"50 1","pages":"135-143"},"PeriodicalIF":0.0000,"publicationDate":"2020-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Коэффициентная устойчивость решений разностных схем, аппроксимирующих смешанные задачи для полулинейных гиперболических уравнений\",\"authors\":\"П. П. Матус, С. В. Лемешевский\",\"doi\":\"10.29235/1561-8323-2020-64-2-135-143\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The stability with respect to coefficients of solution of a difference scheme approximating the initial boundary-value problem for the one-dimensional semi-linear hyperbolic equation is studied. The estimates of the solutions of both differential and difference problems are obtained. In the domain of existence of the solution, the estimates for perturbation of the solution of a difference scheme with respect to perturbation of the coefficients of the equation are obtained. These estimates are consistent with the estimates for the differential problem. In all cases, the method of energy inequalities, the Bihari inequality and its mesh analogue are used.\",\"PeriodicalId\":11227,\"journal\":{\"name\":\"Doklady Akademii nauk\",\"volume\":\"50 1\",\"pages\":\"135-143\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-05-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Doklady Akademii nauk\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.29235/1561-8323-2020-64-2-135-143\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Doklady Akademii nauk","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.29235/1561-8323-2020-64-2-135-143","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Коэффициентная устойчивость решений разностных схем, аппроксимирующих смешанные задачи для полулинейных гиперболических уравнений
The stability with respect to coefficients of solution of a difference scheme approximating the initial boundary-value problem for the one-dimensional semi-linear hyperbolic equation is studied. The estimates of the solutions of both differential and difference problems are obtained. In the domain of existence of the solution, the estimates for perturbation of the solution of a difference scheme with respect to perturbation of the coefficients of the equation are obtained. These estimates are consistent with the estimates for the differential problem. In all cases, the method of energy inequalities, the Bihari inequality and its mesh analogue are used.
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