IJPAM: Volume 113, No. 5 (2017)




N.N. Ermolaeva$^1$, G.V. Krivovichev$^2$,
G.I. Kurbatova$^3$, S.A. Mikheev$^4$
$^{1,2,3,4}$Faculty of Applied Mathematics and Control Processes
Saint-Petersburg State University
7/9 Universitetskaya nab., Saint Petersburg


The problem of mathematical modelling of gas-pipeline glaciation process is considered. The one-dimensional case is presented. Two methods of numerical solution are realized. The first is a front-tracking method with variable time step. The method is realized for initial-boundary value problem with Stefan condition for linear heat equation with unknown moving boundary. Another method is a continuous method based on the solution of the problem for nonlinear heat equation in domain with fixed boundaries and the Dirichlet condition. By the comparison of the results obtained by two methods the optimal values of continuous method parameters are defined. These values may be realized in application of continuous method in multidimensional cases.


Received: December 6, 2016
Revised: March 7, 2017
Published: April 1, 2017

AMS Classification, Key Words

AMS Subject Classification: 35K05, 35K61, 35K60, 65M06, 65Z05.
Key Words and Phrases: Glaciation, modelling, Stefan problem.

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How to Cite?

DOI: 10.12732/ijpam.v113i5.8 How to cite this paper?

International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 113
Issue: 5
Pages: 609 - 616

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