@article{b9556b9c234846d68fb03a947c15d06b, title = "Stability condition for difference schemes for parabolic systems", abstract = "Recently, Goldberg studied in [M. Goldberg, SIAM J. Numer. Anal., 35 (1998), pp. 478-493, M. Goldberg, SIAM J. Numer. Anal., 35 (1998), pp. 1995-2003] stability conditions of a well-known family of difference schemes for the following multidimensional parabolic system of second order: ∂u(x, t)/∂t = ∑1≤p≤q≤s Apq ∂2u(x, t)/∂xp∂xq + ∑1≤p≤s Bp ∂u(x, t)/∂xp + Cu(x, t). Here we present a modified stability condition for the above problem, and prove that this condition is optimal in some sense.", keywords = "Difference schemes, Parabolic systems, Stability", author = "Weiwei SUN and Guangwei Yuan", year = "2000", doi = "10.1137/S0036142998348182", language = "English", volume = "38", pages = "548--555", journal = "SIAM Journal on Numerical Analysis", issn = "0036-1429", publisher = "Society for Industrial and Applied Mathematics", number = "2", }