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

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References | Similar Articles | Additional Information

**[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)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1960-0115283-8

Article copyright:
© Copyright 1960
American Mathematical Society