Abstract
The Peaceman-Rachford finite difference method is applied to cylindrically symmetric, transient heat conduction problems in biological media. Inhomogeneous media and internal sources which vary in both space and time are permitted. Boundary conditions are satisfied without sacrificing high local resolution by means of an exponentially stretched grid. Computation time on a Philco 2000/210 computer is approximately 5 msec per grid point per time step.
Similar content being viewed by others
Literature
Carslaw, H. S. and J. C. Jaeger. 1959.Conduction of Heat in Solids. London: Oxford.
Douglas, J. and J. Gunn. 1964. “A General Formulation of Alternating Direction Methods, I.”Numer. Math.,6, 428–453.
Hildebrand, F. P. 1968.Finite-Difference Equations and Simulations. Englewood Cliffs: Prentice-Hall.
Kunz, K. S. 1957.Numerical Analysis. New York: McGraw-Hill.
Peaceman, D. W. and H. H. Rachford, Jr. 1955. “The Numerical Solution of Parabolic and Elliptic Differential Equations”.J. Soc. Indust. Appl. Math.,3, 28–41.
Saul'yev, V. K. 1964.Integration of Equations of Parabolic Type by the Method of Nets. New York: MacMillan.
Young, D. 1962. “The Numerical Solution of Elliptic and Parabolic Partial Differential Equations”. InSurvey of Numerical Analysis, ed., J. Todd. New York: McGraw-Hill.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mainster, M.A., White, T.J., Tips, J.H. et al. Transient thermal behavior in biological systems. Bulletin of Mathematical Biophysics 32, 303–314 (1970). https://doi.org/10.1007/BF02476870
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02476870