Variable time-step method with coordinate transformation. (English) Zbl 0526.65085


65Z05 Applications to the sciences
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
35R35 Free boundary problems for PDEs
35K05 Heat equation
80A17 Thermodynamics of continua
Full Text: DOI


[1] Crank, J., Two methods for the numerical solution of moving boundary problems in diffusion and heat flow, J. Mech. Appl. Math., 10, 220-231 (1957) · Zbl 0077.32604
[2] Crank, J.; Gupta, R. S., A method for solving moving boundary problems in heat flow using cubic splines or polynomials, J. Inst. Math. Appl., 10, 296-304 (1972) · Zbl 0299.65049
[3] Gupta, R. S., Moving grid method without interpolations, Comput. Meths. Appl. Mech. Engrg., 4, 143-152 (1974) · Zbl 0284.76072
[4] Murray, W. D.; Landis, F., Numerical and machine solutions of transient heat conduction problems involving melting or freezing, J. Heat Transfer, 81, 106-112 (1959)
[5] Douglas, J.; Gallie, T. M., On the numerical integration of a parabolic differential equation subject to a moving boundary condition, Duke Math. J., 22, 557-570 (1955) · Zbl 0066.10503
[6] Gooling, J. S.; Khader, M. S., One dimensional inward solidification with a convective boundary condition, AFS Cast Metals Res. J., 10, 26-29 (1974)
[7] Yuen, W. W.; Kleinman, A. M., Application of a variable time-step finite difference method for the one-dimensional melting problem including the effect of subcooling, AIChE J., 26, 828-832 (1980)
[8] Gupta, R. S.; Kumar, D., A modified variable time step method for the one dimensional Stefan problem, Comput. Meths. Appl. Mech. Engrg., 23, 101-109 (1980) · Zbl 0446.76070
[9] Gupta, R. S.; Kumar, D., Variable time step methods for one-dimensional Stefan problem with mixed boundary condition, Internat. J. Heat Mass Transfer, 24, 251-259 (1981) · Zbl 0462.76095
[10] Gupta, R. S.; Kumar, D., Complete numerical solution of the oxygen diffusion problem involving a moving boundary, Comput. Meths. Appl. Mech. Engrg., 29, 233-239 (1981) · Zbl 0469.65087
[11] Crank, J.; Gupta, R. S., A moving boundary problem arising from the diffusion of oxygen in absorbing tissue, J. Inst. Math. Appl., 10, 19-33 (1972) · Zbl 0247.65064
[12] Hansen, E.; Hougaard, P., On a moving boundary problem from biomechanics, J. Inst. Math. Appl., 13, 385-398 (1974) · Zbl 0307.45016
[13] Ferris, D. H.; Hill, S., On the numerical solution of a one-dimensional diffusion problem with a moving boundary, NPL Rept. NAC, 45 (1974)
[14] Berger, A. E.; Ciment, M.; Rogers, J. C.W., Numerical solution of a diffusion consumption problem with a free boundary, SIAM J. Numer. Anal., 12, 646-672 (1975) · Zbl 0317.65032
[15] Miller, J. V.; Morton, K. W.; Baines, M. J., A finite element moving boundary computation with an adaptive mesh, J. Inst. Math. Appl., 22, 467-477 (1978) · Zbl 0394.65032
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.