{"title":"An explicit modified method of characteristics for the one-dimensional nonstationary convection-diffusion problem with dominating convection","authors":"J. Dalík, H. Růžičková","doi":"10.21136/am.1995.134300","DOIUrl":null,"url":null,"abstract":"We describe a numerical method for the equation $u_t + pu_x - \\varepsilon u_{xx} = f$ in $(0,1) \\times (0,T)$ with Dirichlet boundary and initial conditions which is a combination of the method of characteristics and the finite-difference method. We prove both an a priori local error-estimate of a high order and stability. Example 3.3 indicates that our approximate solutions are disturbed only by a minimal amount of the artificial diffusion.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"183 1","pages":"367-380"},"PeriodicalIF":0.6000,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applications of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.21136/am.1995.134300","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 3
Abstract
We describe a numerical method for the equation $u_t + pu_x - \varepsilon u_{xx} = f$ in $(0,1) \times (0,T)$ with Dirichlet boundary and initial conditions which is a combination of the method of characteristics and the finite-difference method. We prove both an a priori local error-estimate of a high order and stability. Example 3.3 indicates that our approximate solutions are disturbed only by a minimal amount of the artificial diffusion.
期刊介绍：
Applications of Mathematics publishes original high quality research papers that are directed towards applications of mathematical methods in various branches of science and engineering.
The main topics covered include:
- Mechanics of Solids;
- Fluid Mechanics;
- Electrical Engineering;
- Solutions of Differential and Integral Equations;
- Mathematical Physics;
- Optimization;
- Probability
Mathematical Statistics.
The journal is of interest to a wide audience of mathematicians, scientists and engineers concerned with the development of scientific computing, mathematical statistics and applicable mathematics in general.
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