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Solutions of Poisson’s equation in channel-like geometries. (English) Zbl 1001.65131
Summary: Electric forces play a key role in the conductance of ions in biological channels. Therefore, their correct treatment is very important in making physical models of ion channels. Here, we present FORTRAN 90 codes for solution of Poisson’s equation satisfying the Dirichlet boundary conditions in realistic channel geometries that can be used in studies of ion channels. For a general channel shape, we discuss a numerical solution of Poisson’s equation based on an iterative technique. We also provide an analytical solution of Poisson’s equation in toroidal coordinates and its numerical implementation. A torus shaped channel is closer to reality than a cylindrical one, hence it could serve as a useful test model.

##### MSC:
 65N38 Boundary element methods (BVP of PDE) 65N55 Multigrid methods; domain decomposition (BVP of PDE) 78A70 Biological applications of optics and electromagnetic theory 92C30 Physiology (general) 35J05 Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation 65Y15 Packaged methods in numerical analysis
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##### References:
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