Open AccessSPECIAL SPLINE APPROXIMATION FOR THE SOLUTION OF THE NON-STATIONARY 3-D MASS TRANSFER PROBLEM
Author(s) -
Ilmārs Kangro,
Harijs Kalis,
Ērika Teirumnieka,
Edmunds Teirumnieks
Publication year - 2021
Publication title -
vide. tehnoloģija. resursi/environment. technology. resources
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.113
H-Index - 8
eISSN - 2256-070X
pISSN - 1691-5402
DOI - 10.17770/etr2021vol2.6577
Subject(s) - spline (mechanical) , mathematics , perfect spline , boundary value problem , mathematical analysis , domain (mathematical analysis) , fourier series , thin plate spline , spline interpolation , physics , statistics , bilinear interpolation , thermodynamics
In this paper we consider the conservative averaging method (CAM) with special spline approximation for solving the non-stationary 3-D mass transfer problem. The special hyperbolic type spline, which interpolates the middle integral values of piece-wise smooth function is used. With the help of these splines the initial-boundary value problem (IBVP) of mathematical physics in 3-D domain with respect to one coordinate is reduced to problems for system of equations in 2-D domain. This procedure allows reduce also the 2-D problem to a 1-D problem and thus the solution of the approximated problem can be obtained analytically. The accuracy of the approximated solution for the special 1-D IBVP is compared with the exact solution of the studied problem obtained with the Fourier series method. The numerical solution is compared with the spline solution. The above-mentioned method has extensive physical applications, related to mass and heat transfer problems in 3-D domains.