Publication Cover
Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 1, 1978 - Issue 3
20
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Direct and Iterative One-Dimensional Front Tracking Methods for the Two-Dimensional Stefan Problem

Pages 351-364 | Published online: 14 Jul 2010

References

  • Meyer , G. H. 1977 . An Alternating Direction Method for Multidimensional Parabolic Free Surface Problems . Int. J. Numer. Methods Eng. , vol. 11 : 741 – 752 .
  • Heyer , G. H. The Numerical Solution of Stefan Problems with Front Tracking and Smoothing Methods . Appl. Math. Comput. , in press
  • Meyer , G. H. 1969 . An Application of the Method of Lines to Multidimensional Free Boundary Problems . J. Inst. Math. Its Appl. , vol. 20 : 317 – 329 .
  • Yanenko , N. 1977 . The Method of Fractional Steps , Edited by: Holt , M. Berlin : Springer .
  • Budak , B. , Sobol'eva , E. and Uspenskii , A. 1965 . A Difference Method with Coefficient Smoothing for the Solution of Stefan Problems . Zh. Vychisl. Mat. Mat. Fiz. , vol. 5 : 828 – 840 .
  • Samarskii , A. and Moiseyenko , B. 1965 . An Economic Continuous Calculation Scheme for the Stefan Multi-dimensional Problem . Zh. Vychisl. Mat. Mat. Fiz. , vol. 5 : 816 – 927 .
  • Meyer , G. H. 1970 . On a Free Interface Problem for Linear Ordinary Differential Equations and the One Phase Stefan Problem . Numer. Math. , vol. 16 : 248 – 267 .
  • Sachs , A. 1974 . Zur Struktur eines Algorithmus zur Lösung freier Randwertprobleme parabolischer Differenzialoperatoren , vol. 395 , Berlin : Springer . Lecture Notes
  • Jones , D. J. , South , J. C. Jr. and Klunker , E. B. 1972 . On the Numerical Solution of Elliptic Partial Differential Equations by the Method of Lines . J. Comput. Phys. , vol. 9 : 496 – 527 .
  • Liskovets , D. A. 1965 . The Method of Lines . Differential'nye Urav. , vol. 1 : 1662 – 1678 . (Differential Equations, vol. 1, pp. 1308–1323, 1965.)
  • Meyer , G. H. 1978 . The Method of Lines for Poisson's Equation with Nonlinear or Free Boundary Conditions . Numer. Math. , vol. 29 : 329 – 344 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.