Numerical investigations of stochastic Newell-Whitehead-Segel equation in (2+1) dimensions
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Tarih
2023
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
World Scientific Publ Co Pte Ltd
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
The stochastic Newell-Whitehead-Segel in (2+1) dimensions is under consideration. It represents the population density or dimensionless temperature and it discusses how stripes appear in temporal and spatial dimensional systems. The Newell-Whitehead-Segel equation (NWSE) has applications in different areas such as ecology, chemical, mechanical, biology and bio-engineering. The important thing is if we see the problem in the two-dimensional (2D) manifold, then the whole 3D picture can be included in the model. The 3D space is embedded compactly in the 2D manifolds. So, 2D problems for the Newell-White-Segel equation are very important because they consider the one, two and three dimensions in it. The numerical solutions of the underlying model have been extracted successfully by two schemes, namely stochastic forward Euler (SFE) and the proposed stochastic nonstandard finite difference (SNSFD) schemes. The existence of the solution is guaranteed by using the contraction mapping principle and Schauder's fixed-point theorem. The consistency of each scheme is proved in the mean square sense. The stability of the schemes is shown by using von Neumann criteria. The SFE scheme is conditionally stable and the SNSFD scheme is unconditionally stable. The efficacy of the proposed methods is depicted through the simulations. The 2D and 3D graphs are plotted for various values of the parameters.
Açıklama
Anahtar Kelimeler
Stochastic reaction-diffusion equation, unique existence, numerical schemes, simulations
Kaynak
International Journal of Modern Physics B
WoS Q Değeri
Q1
Scopus Q Değeri
Q2
Cilt
37
Sayı
30
