Mori, Yoichiro; Peskin, Charles S. A numerical method for cellular electrophysiology based on the electrodiffusion equations with internal boundary conditions at membranes. (English) Zbl 1182.92024 Commun. Appl. Math. Comput. Sci. 4, 85-134 (2009). Summary: We present a numerical method for solving the system of equations of a model of cellular electrical activity that takes into account both geometrical effects and ionic concentration dynamics. A challenge in constructing a numerical scheme for this model is that its equations are stiff: there is a time scale associated with “diffusion” of the membrane potential that is much faster than the time scale associated with the physical diffusion of ions. We use an implicit discretization in time and a finite volume discretization in space. We present convergence studies of the numerical method for cylindrical and two-dimensional geometries for several cases of physiological interest. Cited in 17 Documents MSC: 92C37 Cell biology 92C05 Biophysics 65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 78A70 Biological applications of optics and electromagnetic theory 35Q92 PDEs in connection with biology, chemistry and other natural sciences 92C30 Physiology (general) Keywords:three-dimensional cellular electrophysiology; electrodiffusion; ephaptic transmission; finite volume method PDFBibTeX XMLCite \textit{Y. Mori} and \textit{C. S. Peskin}, Commun. Appl. Math. Comput. Sci. 4, 85--134 (2009; Zbl 1182.92024) Full Text: DOI