Open AccessStability and errors estimates of a second-order IMSP scheme
Author(s) -
Fasma Diele,
Angela Martiradonna,
Cătălin Trenchea
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2022076
Subject(s) - stability (learning theory) , convergence (economics) , mathematics , order (exchange) , scheme (mathematics) , symplectic geometry , computer science , algorithm , statistical physics , mathematical analysis , physics , finance , machine learning , economics , economic growth
We analyze a second-order accurate implicit-symplectic (IMSP) scheme for reaction-diffusion systems modeling spatiotemporal dynamics of predator-prey populations. We prove stability and errors estimates of the semi-discrete-in-time approximations, under positivity assumptions. The numerical simulations confirm the theoretically derived rates of convergence and show an improved accuracy in the second-order IMSP in comparison with the first-order IMSP, at same computational cost.