## Discrete-in-time random particle blob method for the Keller-Segel equation and convergence analysis

Publication
, Journal Article

Huang, H; Liu, JG

Published in: Communications in Mathematical Sciences

January 1, 2017

We establish an error estimate of a discrete-in-time random particle blob method for the Keller{Segel (KS) equation in ℝd (d≥2). With a blob size ε=N-1/d(d+1) log(N), we prove the convergence rate between the solution to the KS equation and the empirical measure of the random particle method under L2 norm in probability, where N is the number of the particles.

### Duke Scholars

## Published In

Communications in Mathematical Sciences

## DOI

## EISSN

1945-0796

## ISSN

1539-6746

## Publication Date

January 1, 2017

## Volume

15

## Issue

7

## Start / End Page

1821 / 1842

## Related Subject Headings

- Applied Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 1502 Banking, Finance and Investment
- 0102 Applied Mathematics
- 0101 Pure Mathematics

### Citation

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Chicago

ICMJE

MLA

NLM

Huang, H., & Liu, J. G. (2017). Discrete-in-time random particle blob method for the Keller-Segel equation and convergence analysis.

*Communications in Mathematical Sciences*,*15*(7), 1821–1842. https://doi.org/10.4310/CMS.2017.v15.n7.a2Huang, H., and J. G. Liu. “Discrete-in-time random particle blob method for the Keller-Segel equation and convergence analysis.”

*Communications in Mathematical Sciences*15, no. 7 (January 1, 2017): 1821–42. https://doi.org/10.4310/CMS.2017.v15.n7.a2.Huang H, Liu JG. Discrete-in-time random particle blob method for the Keller-Segel equation and convergence analysis. Communications in Mathematical Sciences. 2017 Jan 1;15(7):1821–42.

Huang, H., and J. G. Liu. “Discrete-in-time random particle blob method for the Keller-Segel equation and convergence analysis.”

*Communications in Mathematical Sciences*, vol. 15, no. 7, Jan. 2017, pp. 1821–42.*Scopus*, doi:10.4310/CMS.2017.v15.n7.a2.Huang H, Liu JG. Discrete-in-time random particle blob method for the Keller-Segel equation and convergence analysis. Communications in Mathematical Sciences. 2017 Jan 1;15(7):1821–1842.

## Published In

Communications in Mathematical Sciences

## DOI

## EISSN

1945-0796

## ISSN

1539-6746

## Publication Date

January 1, 2017

## Volume

15

## Issue

7

## Start / End Page

1821 / 1842

## Related Subject Headings

- Applied Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 1502 Banking, Finance and Investment
- 0102 Applied Mathematics
- 0101 Pure Mathematics