Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

A method for calculating solutions of parabolic equations with a free boundary


Author: Milton E. Rose
Journal: Math. Comp. 14 (1960), 249-256
MSC: Primary 65.00; Secondary 80.00
DOI: https://doi.org/10.1090/S0025-5718-1960-0115283-8
MathSciNet review: 0115283
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] J. Crank, ``Two methods for the numerical solution of moving-boundary problems in diffusion and heat flow,'' Quart. Jn. Mech. and Appl. Math., v. 10, 1957, p. 220-231. MR 0085611 (19:66a)
  • [2] J. Douglas, Jr. & T. M. Gallie, Jr., ``On the numerical integration of a parabolic differential equation subject to a moving boundary condition,'' Duke Math. Jn., v. 22, 1955, p. 557-572. MR 0078755 (17:1241j)
  • [3] G. W. Evans, E. Isaacson & J. K. L. Macdonald, ``Stefan-like problems,'' Quart. Appl. Math., v. 8, 1950, p. 312-319. MR 0037451 (12:263f)
  • [4] A. Friedman, ``Free boundary problems for parabolic equations I. Melting of solids,'' Jn. Math. and Mech., v. 8, 1959, p. 499-518. MR 0144078 (26:1626)
  • [5] J. B. Keller, ``Geometrical acoustics I: The theory of weak shock waves,'' Jn. Appl. Phys., v. 25, 1954, p. 938-947. MR 0067654 (16:761e)
  • [6] I. Kolodner, ``Free boundary problems for the heat equation with, application to problems of change of phase,'' Communs. on Pure and Appl. Math., v. 9, 1956, p. 1-32. MR 0087011 (19:285a)
  • [7] P. D. Lax, ``Weak solutions of nonlinear hyperbolic equations and their numerical computations,'' Communs. on Pure and Appl. Math., v. 7, 1954, p. 159-193. MR 0066040 (16:524g)
  • [8] W. Trench, ``On an explicit method for the solution of a Stefan problem,'' Jn., Soc. Ind. and Appl. Math., v. 7, 1959, p. 184-204. MR 0110205 (22:1087)
  • [9] W. T. Kyner, ``An existence and uniqueness theorem for a nonlinear Stefan problem,'' Jn. Math. and Mech., v. 8, 1959, p. 483-498. MR 0144082 (26:1630)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65.00, 80.00

Retrieve articles in all journals with MSC: 65.00, 80.00


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1960-0115283-8
Article copyright: © Copyright 1960 American Mathematical Society

American Mathematical Society