An optimal adaptive time-stepping scheme for solving reaction-diffusion-chemotaxis systems
Reaction-diffusion-chemotaxis systems have proven to be fairlyaccurate mathematical models for many pattern formation problems in chemistryand biology. These systems are important for computer simulationsof patterns, parameter estimations as well as analysis of the biological systems.To solve reacti...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2007-01-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.187 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590300919365632 |
|---|---|
| author | Chichia Chiu Jui-Ling Yu |
| author_facet | Chichia Chiu Jui-Ling Yu |
| author_sort | Chichia Chiu |
| collection | DOAJ |
| description | Reaction-diffusion-chemotaxis systems have proven to be fairlyaccurate mathematical models for many pattern formation problems in chemistryand biology. These systems are important for computer simulationsof patterns, parameter estimations as well as analysis of the biological systems.To solve reaction-diffusion-chemotaxis systems, efficient and reliablenumerical algorithms are essential for pattern generations. In this paper, ageneral reaction-diffusion-chemotaxis system is considered for specific numericalissues of pattern simulations. We propose a fully explicit discretizationcombined with a variable optimal time step strategy for solving the reactiondiffusion-chemotaxis system. Theorems about stability and convergence of thealgorithm are given to show that the algorithm is highly stable and efficient.Numerical experiment results on a model problem are given for comparisonwith other numerical methods. Simulations on two real biological experimentswill also be shown. |
| format | Article |
| id | doaj-art-feea3f06bf1746ca8f0123e71aee9465 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-feea3f06bf1746ca8f0123e71aee94652025-01-24T01:53:27ZengAIMS PressMathematical Biosciences and Engineering1551-00182007-01-014218720310.3934/mbe.2007.4.187An optimal adaptive time-stepping scheme for solving reaction-diffusion-chemotaxis systemsChichia Chiu0Jui-Ling Yu1Department of Mathematics, Michigan State University, East Lansing, MI 48864Department of Mathematics, Michigan State University, East Lansing, MI 48864Reaction-diffusion-chemotaxis systems have proven to be fairlyaccurate mathematical models for many pattern formation problems in chemistryand biology. These systems are important for computer simulationsof patterns, parameter estimations as well as analysis of the biological systems.To solve reaction-diffusion-chemotaxis systems, efficient and reliablenumerical algorithms are essential for pattern generations. In this paper, ageneral reaction-diffusion-chemotaxis system is considered for specific numericalissues of pattern simulations. We propose a fully explicit discretizationcombined with a variable optimal time step strategy for solving the reactiondiffusion-chemotaxis system. Theorems about stability and convergence of thealgorithm are given to show that the algorithm is highly stable and efficient.Numerical experiment results on a model problem are given for comparisonwith other numerical methods. Simulations on two real biological experimentswill also be shown.https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.187equationschemotaxissystemsreactionexplicit methods.diffusionpattern formation problems |
| spellingShingle | Chichia Chiu Jui-Ling Yu An optimal adaptive time-stepping scheme for solving reaction-diffusion-chemotaxis systems Mathematical Biosciences and Engineering equations chemotaxis systems reaction explicit methods. diffusion pattern formation problems |
| title | An optimal adaptive time-stepping scheme for solving reaction-diffusion-chemotaxis systems |
| title_full | An optimal adaptive time-stepping scheme for solving reaction-diffusion-chemotaxis systems |
| title_fullStr | An optimal adaptive time-stepping scheme for solving reaction-diffusion-chemotaxis systems |
| title_full_unstemmed | An optimal adaptive time-stepping scheme for solving reaction-diffusion-chemotaxis systems |
| title_short | An optimal adaptive time-stepping scheme for solving reaction-diffusion-chemotaxis systems |
| title_sort | optimal adaptive time stepping scheme for solving reaction diffusion chemotaxis systems |
| topic | equations chemotaxis systems reaction explicit methods. diffusion pattern formation problems |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.187 |
| work_keys_str_mv | AT chichiachiu anoptimaladaptivetimesteppingschemeforsolvingreactiondiffusionchemotaxissystems AT juilingyu anoptimaladaptivetimesteppingschemeforsolvingreactiondiffusionchemotaxissystems AT chichiachiu optimaladaptivetimesteppingschemeforsolvingreactiondiffusionchemotaxissystems AT juilingyu optimaladaptivetimesteppingschemeforsolvingreactiondiffusionchemotaxissystems |