On Conservative Averaging Method in Spline Applications

  • Harijs Kalis Латвийский университет
  • Ilmars Ilmars Резекненская академия технологий


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 reduce 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 are obtained with CAM. The numerical solution is compared with the analytical solution.

Сведения об авторах

Harijs Kalis, Латвийский университет

заведующий кафедрой дифференциальных уравнений и численных методов, Институт математики и компьютерных наук

Ilmars Ilmars, Резекненская академия технологий

Faculty of Engineering

Как цитировать
KALIS, Harijs; ILMARS, Ilmars. On Conservative Averaging Method in Spline Applications. Международный научный журнал «Современные информационные технологии и ИТ-образование», [S.l.], v. 16, n. 1, may 2020. ISSN 2411-1473. Доступно на: <http://sitito.cs.msu.ru/index.php/SITITO/article/view/623>. Дата доступа: 09 aug. 2020
Теоретические вопросы информатики, прикладной математики, компьютерных наук