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Abstract: In the current paper a numerical approach is presented for solving a system of coupled gradient-diffusion equations which acts as a first model for the growth of axons in brain tissue. The presented approach can be applied to a much wider range of problems, but we focus on the axon growth problem. In our approach time stepping is performed with a Rosen brock solver with approximate matrix factorization. For the JacobJan an approximation is used that simplifies the solution of the coupled... (Update)
Context of citations to this paper: More
.... are ordinary differential equations (ODEs) The model will be solved numerically, using techniques similar to those used in [7] see also [3]) For the spatial discretization of the parabolic equations we use standard second order finite differences. The gradients are...
...and source terms with respect to bundling and debundling. A similar conclusion was reported in a second numerical paper by Lastdrager [3]. Therefore we want to gain understanding on the relative importance of parameters, the sensitivity of the dynamics with respect to these...
Cited by: More
On the Dynamics of a Mixed Parabolic-Gradient System - Krottje (2002) (Correct)
Parallel Simulation of Axon Growth in the Nervous System - Wensch, Sommeijer (2002) (Correct)
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2: A numerical study of mixed parabolic-gradient systems - Verwer, Sommeijer - 2001
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BibTeX entry: (Update)
B. Lastdrager, Numerical solution of mixed gradient-diffusion equations modelling axon growth, CWI, Report MAS-R0203 (2002). http://citeseer.ist.psu.edu/lastdrager02numerical.html More
@misc{ lastdrager02numerical,
author = "B. Lastdrager",
title = "Numerical solution of mixed gradient-diffusion equations modelling axon
growth",
text = "B. Lastdrager, Numerical solution of mixed gradient-diffusion equations
modelling axon growth, CWI, Report MAS-R0203 (2002).",
year = "2002",
url = "citeseer.ist.psu.edu/lastdrager02numerical.html" }
Citations (may not include all citations):191 Solving ordinary differential equations II (context) - Hairer, Wanner - 1996
27 An implicit finite-difference algorithm for hyperbolic syste.. (context) - Beam, Warming - 1976
9 A second-order Rosenbrock method applied to photochemical di.. (context) - Verwer, Spee et al. - 1999
4 Diffusion in axon guidance (context) - Goodhill - 1997
4 Approximate factorization for time-dependent partial differe.. (context) - van der Houwen, Sommeijer - 2000
3 A numerical study of mixed parabolic-gradient systems - Verwer, Sommeijer - 2001
1 Models of axon guidance during development (context) - Hentschel, van Ooyen - 1999
1 Solution of time-dependent advection-diffusion problems with.. - Lastdrager, Koren et al. - 2001
1 Difference systems of second order accuracy with a divided o.. (context) - D'yakonov - 1964
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