Hostname: page-component-76fb5796d-qxdb6 Total loading time: 0 Render date: 2024-04-29T15:52:42.053Z Has data issue: false hasContentIssue false
  • English
  • Français

On the solution of a nonlinear problem in cell membrane theory

Published online by Cambridge University Press:  17 February 2009

A. M. Arthurs  and
J. Clegg
J. Clegg
Affiliation:
Department of Mathematics, University of York, England
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Methods for integral equations are used to derive upper and lower pointwise bounds for the solution of a nonlinear boundary value problem arising in the steady-state finite cable model of cell membranes. Test calculations are performed to illustrate the results and the accuracy achieved is significantly better than that obtained previously by other methods.

Type
Research Article
Information
The ANZIAM Journal , Volume 36 , Issue 1 , July 1994 , pp. 26 - 37
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Anderson, N. and Arthurs, A. M., “Complementary variational principles for the steady-state finite cable model of nerve membranes”, Bull. Math. Biol. 40 (1978) 735–742.CrossRefGoogle ScholarPubMed
[2]Arthurs, A. M. and Arthurs, W. M., “Pointwise bounds for the solution of a nonlinear problem in cell membrane theory”, Bull. Math. Biol. 45 (1983) 155–168.CrossRefGoogle ScholarPubMed
[3]Jack, J. J. B., Noble, D. and Tsien, R. W., Electric current flow in excitable cells (Clarendon Press, Oxford, 1975).Google Scholar
[4]Kootsey, J. M., “The steady-state finite cable: numerical method for non-linear membrane”, J. Theor. Biol. 64 (1977) 413–420.CrossRefGoogle ScholarPubMed
[5]Robinson, P. D. and Yuen, P. K., “Bivariational methods for Hammerstein integral equations”, IMA J. App. Math. 39 (1987) 177–188.CrossRefGoogle Scholar
[6]Stakgold, I., Boundary value problems of mathematical physics, Volume 1 (The Macmillan Co., New York, 1967).Google Scholar