IJPAM: Volume 87, No. 1 (2013)

COMPUTATIONAL STUDY OF
TWO-PHASE STEFAN PROBLEM IN A FINITE INTERVAL

Daniel Lee
Department of Applied Mathematics
Tunghai University
Taichung, 40704, TAIWAN, R.O.C.


Abstract. We consider in this work the heat diffusion of one-dimensional spatial variable in finite domains. Two finite interval models are derived from relevant models in the semi-infinite interval. We investigate both static and dynamic grid approaches in fixed coordinates. Numerical discretizations based on finite differences or spectral differentiations are applied. For each computational model we discuss the numerical methods and the issues in software design and the trade-offs between accuracy and efficiency. In particular, we discuss a control variable (the scale factor) for achieving appropriate grid distribution and therefore better accuracy and run-time efficiency. The observations can be helpful in practical applications for which no explicit solution is expected.

Received: April 16, 2013

AMS Subject Classification: 65-05, 65M06

Key Words and Phrases: heat transfer, Stefan problem, spline, collocation

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DOI: 10.12732/ijpam.v87i1.3 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: 2013
Volume: 87
Issue: 1