Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- Nonlinear Dynamics in Partial Differential Equations, S. Ei, S. Kawashima, M. Kimura and T. Mizumachi, eds. (Tokyo: Mathematical Society of Japan, 2015), 243 - 251
Numerical solution of nonlinear cross-diffusion systems by a linear scheme
Abstract
This paper introduces a linear scheme to approximate the solutions of the general nonlinear cross-diffusion system. After discretizing the scheme in space, we obtain a versatile, easy to implement and stable numerical scheme for the cross-diffusion system. Numerical experiments are carried out to examine rates of convergence with respect to the time step and the spatial mesh sizes.
Article information
Dates
Received: 20 April 2012
Revised: 29 January 2013
First available in Project Euclid:
30 October 2018
Permanent link to this document
https://projecteuclid.org/
euclid.aspm/1540934220
Digital Object Identifier
doi:10.2969/aspm/06410243
Mathematical Reviews number (MathSciNet)
MR3381209
Zentralblatt MATH identifier
1337.65117
Subjects
Primary: 35K55: Nonlinear parabolic equations 35K57: Reaction-diffusion equations 65M12: Stability and convergence of numerical methods 92D25: Population dynamics (general)
Keywords
Cross-diffusion systems nonlinear diffusion discrete-time schemes numerical schemes
Citation
Murakawa, Hideki. Numerical solution of nonlinear cross-diffusion systems by a linear scheme. Nonlinear Dynamics in Partial Differential Equations, 243--251, Mathematical Society of Japan, Tokyo, Japan, 2015. doi:10.2969/aspm/06410243. https://projecteuclid.org/euclid.aspm/1540934220
