Title

FUNDAMENTAL SOLUTIONS METHOD FOR COUPLED
MATHEMATICAL MODELS OF HEAT AND
MASS TRANSFERS

Authors

V. Gorbachenko, O. Yaremko, N. Yaremko, M. Alkazweeny
Penza State University
st. Krasnaya, 40, Penza, 440038, RUSSIA

Abstract

We extend the fundamental solutions method into the case of the Cauchy problem for the systems of heat equations on the real axis. We use an approach the fundamental solution of which is replaced by fundamental matrix. Vector function approximation problem appears by using a weighted sum of the fundamental kernel matrices. A weighted sum is understood as the sum of product for the fundamental kernel matrices and the unknown weighted vector coefficients. Setting weighted vector coefficients, center and window width of each Gaussian carried out by the method of least squares. We consider one more way of vector function approximation. This method consists in the fact that we replace the vector Cauchy problem into n disjoint Cauchy problems, then we find an approximation of each scalar problem and the solution of a vector problem. Vector Cauchy problem for the heat equation on the real line with n division points to a multilayer medium is solved. Initial conditions are approximated by a weighted sum of the fundamental kernel matrices satisfying conjugate conditions. The fundamental matrix on the right infinite interval is chosen to be the fundamental matrix for single occasion. The fundamental matrix is uniquely determined by conjugate conditions on the remaining intervals.

History

Received: 2017-09-12
Revised: 2018-01-25
Published: April 13, 2018

AMS Classification, Key Words

AMS Subject Classification:
Key Words and Phrases: fundamental solution, fundamental matrix, kernel basis function, Gaussian, approximation of functions

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How to Cite?

DOI: 10.12732/ijpam.v118i3.12 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2018
Volume: 118
Issue: 3
Pages: 637 - 649

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