Numerical Study of a Chemotaxis System with Non-Linear Boundary Conditions
DOI:
https://doi.org/10.11145/137Abstract
A mathematical model for haematopoietic stem cells migration towards their niche in the bone marrow has been proposed in the literature. It consists of a chemotaxis system of partial differential equations (PDEs) with non-linear boundary conditions and an additional ordinary differential equation on a part of the computational boundary. Various classical numerical methods applied directly to this system may lead to numerical instabilities and loss of the positivity property of the solution, as illustratedin [1]. Finite volume method with appropriate flux limiter and time integration scheme can be used to ensure positivity and non-oscillatory nature of the numerical solution. The non-linear boundary conditions require specific approximation (proposed in [2] for the considered system of PDEs) of the unknown functions when the finite volumes close to the boundaryare treated. The aim in the current study is to extend the theoretical results in [2] with numerical experiments and analysis of the properties of the numerical method. Ongoing results for various sets of parameters (e.g.chemotactic sensitivity function, flux limiter, time/space mesh size) will be presented.
References
[1] G. Bencheva, Computer modelling of haematopoietic stem cells migration, Computers and Mathematics with Applications 64(3) 337–349.
[2] G. Bencheva, On the choice of limiters in a numerical approximation of a chemotaxis system with non-linear boundary conditions, AIP Confer-ence Proceedings 1487 305–313.
Downloads
Published
Issue
Section
License
The journal Biomath Communications is an open access journal. All published articles are immeditely available online and the respective DOI link activated. All articles can be access for free and no reader registration of any sort is required. No fees are charged to authors for article submission or processing. Online publications are funded through volunteer work, donations and grants.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
