# SPECIAL SPLINE APPROXIMATION FOR THE SOLUTION OF THE NON-STATIONARY 3-D MASS TRANSFER PROBLEM

## DOI:

https://doi.org/10.17770/etr2021vol2.6577## Keywords:

conservative averaging method, 3-D mass transfer problem, hyperbolic type splines, analytical solution## Abstract

*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.*

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*ETR*, vol. 2, pp. 69–73, Jun. 2021, doi: 10.17770/etr2021vol2.6577.