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On the convergence of difference schemes for a heat conduction equation
Author(s) -
Andreev Andrey,
Juboury Hussain
Publication year - 1994
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1680010303
Subject(s) - mathematics , convergence (economics) , heat equation , sequence (biology) , thermal conduction , compact convergence , convergence tests , mathematical analysis , relativistic heat conduction , modes of convergence (annotated index) , normal convergence , cauchy distribution , rate of convergence , pure mathematics , heat transfer , key (lock) , heat flux , materials science , isolated point , economic growth , ecology , topological vector space , composite material , biology , genetics , topological space , thermodynamics , physics , economics
Sufficient conditions are obtained for the convergence of difference schemes for the numerical solution of the Cauchy problem for a heat conduction equation in two space variables. The sufficient conditions are derived in a form similar to those for the convergence of a sequence of linear positive operators in the Korovkin theorem. As an application it is shown that difference schemes that are widely used in practice can easily be checked for convergence by these conditions.