Reduced Order Modelling of Shigesada-Kawasaki-Teramoto Cross-Diffusion Systems

Gülden Mülayim

doi:10.33187/jmsm.1234247

EN

Reduced Order Modelling of Shigesada-Kawasaki-Teramoto Cross-Diffusion Systems

Abstract

Shigesada-Kawasaki-Teramoto (SKT) is the most known equation in population ecology for nonlinear cross-diffusion systems. The full order model (FOM) of the SKT system is constructed using symmetric interior penalty discontinuous Galerkin method (SIPG) in space and the semi-implicit Euler method in time. The reduced order models (ROMs) are solved using proper orthogonal decomposition (POD) Galerkin projection. Discrete empirical interpolation method (DEIM) is used to solve the nonlinearities of the SKT system. Numerical simulations show the accuracy and efficiency of the POD and POD-DEIM reduced solutions for the SKT system.

Keywords

discontinuous Galerkin method, discrete empirical interpolation method, proper orthogonal decomposition, Shigesada-Kawasaki-Teramoto equation

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Gülden Mülayim ^*
0000-0001-8952-7658
Türkiye

Publication Date

August 7, 2023

Submission Date

January 14, 2023

Acceptance Date

March 6, 2023

Published in Issue

Year 2023 Volume: 6 Number: 2

DOI

https://doi.org/10.33187/jmsm.1234247

IZ

https://izlik.org/JA97KB79MD

APA

Mülayim, G. (2023). Reduced Order Modelling of Shigesada-Kawasaki-Teramoto Cross-Diffusion Systems. Journal of Mathematical Sciences and Modelling, 6(2), 42-48. https://doi.org/10.33187/jmsm.1234247

AMA

1.Mülayim G. Reduced Order Modelling of Shigesada-Kawasaki-Teramoto Cross-Diffusion Systems. Journal of Mathematical Sciences and Modelling. 2023;6(2):42-48. doi:10.33187/jmsm.1234247

Chicago

Mülayim, Gülden. 2023. “Reduced Order Modelling of Shigesada-Kawasaki-Teramoto Cross-Diffusion Systems”. Journal of Mathematical Sciences and Modelling 6 (2): 42-48. https://doi.org/10.33187/jmsm.1234247.

EndNote

Mülayim G (August 1, 2023) Reduced Order Modelling of Shigesada-Kawasaki-Teramoto Cross-Diffusion Systems. Journal of Mathematical Sciences and Modelling 6 2 42–48.

IEEE

[1]G. Mülayim, “Reduced Order Modelling of Shigesada-Kawasaki-Teramoto Cross-Diffusion Systems”, Journal of Mathematical Sciences and Modelling, vol. 6, no. 2, pp. 42–48, Aug. 2023, doi: 10.33187/jmsm.1234247.

ISNAD

Mülayim, Gülden. “Reduced Order Modelling of Shigesada-Kawasaki-Teramoto Cross-Diffusion Systems”. Journal of Mathematical Sciences and Modelling 6/2 (August 1, 2023): 42-48. https://doi.org/10.33187/jmsm.1234247.

JAMA

1.Mülayim G. Reduced Order Modelling of Shigesada-Kawasaki-Teramoto Cross-Diffusion Systems. Journal of Mathematical Sciences and Modelling. 2023;6:42–48.

MLA

Mülayim, Gülden. “Reduced Order Modelling of Shigesada-Kawasaki-Teramoto Cross-Diffusion Systems”. Journal of Mathematical Sciences and Modelling, vol. 6, no. 2, Aug. 2023, pp. 42-48, doi:10.33187/jmsm.1234247.

Vancouver

1.Gülden Mülayim. Reduced Order Modelling of Shigesada-Kawasaki-Teramoto Cross-Diffusion Systems. Journal of Mathematical Sciences and Modelling. 2023 Aug. 1;6(2):42-8. doi:10.33187/jmsm.1234247