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Analysis of difference diagrams stability approximating a class of one‐ and two‐dimensional non‐linear–parabolic field equations
Author(s) -
Wiak Slawomir
Publication year - 1989
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620280903
Subject(s) - stability (learning theory) , mathematics , vector field , mathematical analysis , field (mathematics) , vector potential , electromagnetic field , class (philosophy) , magnetic field , pure mathematics , physics , geometry , computer science , quantum mechanics , machine learning , artificial intelligence
This paper describes the stability conditions for difference diagrams applied to the approximation of one‐ and two‐dimensional non‐linear field equations. The one‐dimensional electromagnetic field is described by vector B and vector E , and the two‐dimensional field by magnetic vector potential A . It has been proved that the presence of a lower order of derivatives has a decisive influence on the stability condition of the considered diagrams.