On Conservative Averaging Method in Spline Applications
We consider the conservative averaging method for solving the 3-D boundary-value problem of second order in multilayer domain. Looking back to the history of mathematics, integral parabolic splines relates to conservative averaging method (CAM) introduced by A. Kneser in 1914. In 1980's, A. Bui...
| Main Authors: | , |
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| Format: | Article |
| Language: | Russian |
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The Fund for Promotion of Internet media, IT education, human development «League Internet Media»
2020-05-01
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| Series: | Современные информационные технологии и IT-образование |
| Subjects: | |
| Online Access: | http://sitito.cs.msu.ru/index.php/SITITO/article/view/623 |
| _version_ | 1818972748207095808 |
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| author | Harijs Kalis Ilmars Kangro |
| author_facet | Harijs Kalis Ilmars Kangro |
| author_sort | Harijs Kalis |
| collection | DOAJ |
| description | We consider the conservative averaging method for solving the 3-D boundary-value problem of second order in multilayer domain. Looking back to the history of mathematics, integral parabolic splines relates to conservative averaging method (CAM) introduced by A. Kneser in 1914. In 1980's, A. Buikis had developed CAM method for partial differential equations with discontinuous coefficients, when he was modelling processes in environments with a layered structure. The special hyperbolic and exponential type splines, with middle integral values of piecewise smooth function interpolation, are considered. Using these type splines, the problems of mathematical physics in 3-D with piecewise coefficients are reduced to 2-D problems with respect to one coordinate. This procedure also allows reducing the 2-D problems to 1-D problems and the solution of the approximated problems can be obtained analytically. In the case of constant piecewise coefficients, we obtain the exact discrete approximation of a steady-state 1-D boundary-value problem. Similarly, the approximation of the 3-D nonstationary problem is obtained with CAM. The numerical solution is compared with the analytical solution. |
| first_indexed | 2024-12-20T15:13:12Z |
| format | Article |
| id | doaj.art-c71f56b65d9440909eac2d09d4963e7c |
| institution | Directory Open Access Journal |
| issn | 2411-1473 |
| language | Russian |
| last_indexed | 2024-12-20T15:13:12Z |
| publishDate | 2020-05-01 |
| publisher | The Fund for Promotion of Internet media, IT education, human development «League Internet Media» |
| record_format | Article |
| series | Современные информационные технологии и IT-образование |
| spelling | doaj.art-c71f56b65d9440909eac2d09d4963e7c2022-12-21T19:36:16ZrusThe Fund for Promotion of Internet media, IT education, human development «League Internet Media»Современные информационные технологии и IT-образование2411-14732020-05-01161334010.25559/SITITO.16.202001.33-40On Conservative Averaging Method in Spline ApplicationsHarijs Kalis0https://orcid.org/0000-0002-9438-2614Ilmars Kangro1https://orcid.org/0000-0001-6413-5308University of LatviaRezekne Academy of TechnologiesWe consider the conservative averaging method for solving the 3-D boundary-value problem of second order in multilayer domain. Looking back to the history of mathematics, integral parabolic splines relates to conservative averaging method (CAM) introduced by A. Kneser in 1914. In 1980's, A. Buikis had developed CAM method for partial differential equations with discontinuous coefficients, when he was modelling processes in environments with a layered structure. The special hyperbolic and exponential type splines, with middle integral values of piecewise smooth function interpolation, are considered. Using these type splines, the problems of mathematical physics in 3-D with piecewise coefficients are reduced to 2-D problems with respect to one coordinate. This procedure also allows reducing the 2-D problems to 1-D problems and the solution of the approximated problems can be obtained analytically. In the case of constant piecewise coefficients, we obtain the exact discrete approximation of a steady-state 1-D boundary-value problem. Similarly, the approximation of the 3-D nonstationary problem is obtained with CAM. The numerical solution is compared with the analytical solution.http://sitito.cs.msu.ru/index.php/SITITO/article/view/623special splinesaveraging method3d problemanalytical solution |
| spellingShingle | Harijs Kalis Ilmars Kangro On Conservative Averaging Method in Spline Applications Современные информационные технологии и IT-образование special splines averaging method 3d problem analytical solution |
| title | On Conservative Averaging Method in Spline Applications |
| title_full | On Conservative Averaging Method in Spline Applications |
| title_fullStr | On Conservative Averaging Method in Spline Applications |
| title_full_unstemmed | On Conservative Averaging Method in Spline Applications |
| title_short | On Conservative Averaging Method in Spline Applications |
| title_sort | on conservative averaging method in spline applications |
| topic | special splines averaging method 3d problem analytical solution |
| url | http://sitito.cs.msu.ru/index.php/SITITO/article/view/623 |
| work_keys_str_mv | AT harijskalis onconservativeaveragingmethodinsplineapplications AT ilmarskangro onconservativeaveragingmethodinsplineapplications |