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Some remarks on the renormalization group and Chapman‐Enskog type methods in singularly perturbed problems
Author(s) -
Banasiak Jacek
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6273
Subject(s) - mathematics , renormalization group , asymptotic expansion , class (philosophy) , type (biology) , mathematical physics , renormalization , group (periodic table) , method of matched asymptotic expansions , mathematical analysis , physics , differential equation , quantum mechanics , ecology , artificial intelligence , computer science , biology
In this paper, we show that for a large class of singularly perturbed problems, the classical Chapman‐Enskog asymptotic procedure leads, in a shorter way, to the same asymptotic expansion as the renormalization group (RG) approach. We also prove that the Chapman‐Enskog expansion gives the expected error estimates uniformly on [ 0 , ∞ ) .