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Mathematical Problems in Engineering
Volume 2012, Article ID 791026, 10 pages
Research Article

The Analytical and a Higher-Accuracy Numerical Solution of a Free Boundary Problem in a Class of Discontinuous Functions

Department of Mathematics and Computing, Beykent University, 34396 Istanbul, Turkey

Received 8 July 2011; Revised 10 September 2011; Accepted 8 October 2011

Academic Editor: Ezzat G. Bakhoum

Copyright © 2012 Bahaddin Sinsoysal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. G. I. Barenblatt and M. I. Višik, “On finite velocity of propagation in problems of non-stationary filtration of a liquid or gas,” Prikladnaja Matematika i Mehanika, vol. 20, pp. 411–417, 1956. View at Google Scholar
  2. S. N. Antoncev, “On the localization of solutions of non-linear degenerate elliptic and parabolic equations,” Soviet Mathematics. Doklady, vol. 24, pp. 420–424, 1981. View at Google Scholar
  3. L. K. Martinson and K. B. Pavlov, “On the problem of spatial localization of thermal perturbations in the theory of non-linear heat conduction,” USSR Computational Math and Math Physics, vol. 12, no. 4, pp. 261–268, 1972. View at Google Scholar
  4. S. L. Kamenomostskaya, “On Stefan’s problem,” Mathematics Sbornik, vol. 53, pp. 489–514, 1961. View at Google Scholar
  5. O. A. Oleĭnik, “A method of solution of the general Stefan problem,” Soviet Mathematics. Doklady, vol. 1, pp. 1350–1354, 1960. View at Google Scholar
  6. A. A. Abramov and A. N. Gaipova, “On the numerical solution of some sets of differential equations for problems of Stefan's type,” USSR Computational Mathematics and Mathematical Physics, vol. 11, no. 1, pp. 162–170, 1971. View at Google Scholar · View at Scopus
  7. V. F. Baklanovskaya, “The numerical solution of a nonstationary filtration problem,” USSR Computational Mathematics and Mathematical Physics, vol. 1, no. 1, pp. 114–122, 1962. View at Google Scholar
  8. B. M. Budak and A. B. Uspenskii, “A difference method with front straightening for solving Stefan-type problems,” USSR Computational Mathematics and Mathematical Physics, vol. 9, no. 6, pp. 83–103, 1969. View at Google Scholar · View at Scopus
  9. M. A. Rasulov, “A numerical method of solving a parabolic equation with degeneration,” Differential Equations, vol. 18, no. 8, pp. 1418–1427, 1992. View at Google Scholar
  10. B. Sinsoysal, “A new numerical method for Stefan-type problems in a class of unsmooth functions,” International Journal of Contemporary Mathematical Sciences, vol. 5, no. 27, pp. 1323–1335, 2010. View at Google Scholar · View at Zentralblatt MATH