Numerical Approach to a Nonlocal Advection-Reaction-Diffusion Model of Cartilage Pattern Formation
| Autor: | Jianying Zhang, Tilmann Glimm |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
0301 basic medicine
Discretization Basis function lcsh:QA75.5-76.95 advection-reaction-diffusion systems Integrating factor 03 medical and health sciences symbols.namesake 0302 clinical medicine pattern formation Applied mathematics Boundary value problem Mathematics lcsh:T57-57.97 lcsh:Mathematics Applied Mathematics Method of lines General Engineering Finite difference radial basis functions lcsh:QA1-939 Computational Mathematics Nonlinear system models of chondrogenesis 030104 developmental biology cell-cell adhesion 030220 oncology & carcinogenesis Dirichlet boundary condition lcsh:Applied mathematics. Quantitative methods symbols lcsh:Electronic computers. Computer science |
| Zdroj: | Mathematical and Computational Applications, Vol 25, Iss 36, p 36 (2020) Mathematical and Computational Applications Volume 25 Issue 2 |
| ISSN: | 2297-8747 |
| DOI: | 10.3390/mca25020036 |
| Popis: | We propose a numerical approach that combines a radial basis function (RBF) meshless approximation with a finite difference discretization to solve a nonlinear system of integro-differential equations. The equations are of advection-reaction-diffusion type modeling the formation of pre-cartilage condensations in embryonic chicken limbs. The computational domain is four dimensional in the sense that the cell density depends continuously on two spatial variables as well as two structure variables, namely membrane-bound counterreceptor densities. The biologically proper Dirichlet boundary conditions imposed in the semi-infinite structure variable region is in favor of a meshless method with Gaussian basis functions. Coupled with WENO5 finite difference spatial discretization and the method of integrating factors, the time integration via method of lines achieves optimal complexity. In addition, the proposed scheme can be extended to similar models with more general boundary conditions. Numerical results are provided to showcase the validity of the scheme. |
| Databáze: | OpenAIRE |
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