High-order positivity-preserving hybrid finite-volume-finite-difference methods for chemotaxis systems

Chertock, Alina1; Epshteyn, Yekaterina2; Hu, Hengrui1; Kurganov, Alexander3,4

2018-02

10.1007/s10444-017-9545-9

ADVANCES IN COMPUTATIONAL MATHEMATICS   Impact Factor & Quartile

1019-7168

1572-9044

Chemotaxis refers to mechanisms by which cellular motion occurs in response to an external stimulus, usually a chemical one. Chemotaxis phenomenon plays an important role in bacteria/cell aggregation and pattern formation mechanisms, as well as in tumor growth. A common property of all chemotaxis systems is their ability to model a concentration phenomenon that mathematically results in rapid growth of solutions in small neighborhoods of concentration points/curves. The solutions may blow up or may exhibit a very singular, spiky behavior. There is consequently a need for accurate and computationally efficient numerical methods for the chemotaxis models. In this work, we develop and study novel high-order hybrid finite-volume-finite-difference schemes for the Patlak-Keller-Segel chemotaxis system and related models. We demonstrate high-accuracy, stability and computational efficiency of the proposed schemes in a number of numerical examples.

Patlak-Keller-Segel chemotaxis system Advection-diffusion-reaction systems High-order finite-difference Finite-volume methods Positivity-preserving algorithms

SCI

English

Others

NSF[DMS-1521051] ; NSF[DMS-1521009]

Mathematics

Mathematics, Applied

WOS:000423693000013

SPRINGER

MATHEMATICS

Web of Science

1.North Carolina State Univ, Dept Math, Raleigh, NC 27695 USA
2.Univ Utah, Dept Math, Salt Lake City, UT 84112 USA
3.Southern Univ Sci & Technol China, Dept Math, Shenzhen 518055, Peoples R China
4.Tulane Univ, Dept Math, New Orleans, LA 70118 USA

Chertock, Alina,Epshteyn, Yekaterina,Hu, Hengrui,et al. High-order positivity-preserving hybrid finite-volume-finite-difference methods for chemotaxis systems[J]. ADVANCES IN COMPUTATIONAL MATHEMATICS,2018,44(1):327-350.

Chertock, Alina,Epshteyn, Yekaterina,Hu, Hengrui,&Kurganov, Alexander.(2018).High-order positivity-preserving hybrid finite-volume-finite-difference methods for chemotaxis systems.ADVANCES IN COMPUTATIONAL MATHEMATICS,44(1),327-350.

Chertock, Alina,et al."High-order positivity-preserving hybrid finite-volume-finite-difference methods for chemotaxis systems".ADVANCES IN COMPUTATIONAL MATHEMATICS 44.1(2018):327-350.