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Gupta, Radhey S.; Kumar, Dhirendra

Complete numerical solution of the oxygen diffusion problem involving a moving boundary. (English) Zbl 0469.65087

Comput. Methods Appl. Mech. Eng. 29, 233-239 (1981).
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Cited in 9 Documents

MSC:

65Z05 Applications to the sciences
76Z05 Physiological flows
92Cxx Physiological, cellular and medical topics
35K05 Heat equation
35R35 Free boundary problems for PDEs

Keywords:

numerical results; oxygen diffusion; blood stream; moving boundary problem; variable time step methods

Citations:

Zbl 0247.65064
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\textit{R. S. Gupta} and \textit{D. Kumar}, Comput. Methods Appl. Mech. Eng. 29, 233--239 (1981; Zbl 0469.65087)
Full Text: DOI

References:

[1] 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
[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] Hansen, E.; Hougaard, P., On a moving boundary problem from biomechanics, J. Inst. Math. Appl., 13, 385-398 (1974) · Zbl 0307.45016
[5] Ferris, D. H.; Hill, S., On the numerical solution of a one-dimensional diffusion problem with a moving boundary, NPL Rept. NAC, 45 (1974)
[6] 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
[7] 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
[8] (Ockendon, J. R.; Hodgkins, W. R., Moving Boundary Problems in Heat Flow and Diffusion (1975), Clarendon: Clarendon Oxford) · Zbl 0295.76064
[9] Furzeland, R. M., A survey of the formulation and solution of free and moving boundary (Stefan) problems, Brunel Univ. Tech. Rept. TR/76 (1977) · Zbl 0367.65050
[10] 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
[11] Gooding, J. S.; Khader, M. S., One dimensional inward solidification with a convective boundary condition, AFS Cast Metals Res. J., 10, 26-29 (1974)
[12] 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
[13] 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
[14] 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)
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