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A WELL‐CONDITIONED MATRIX FOR ( ku X ) X WITH DISCONTINUOUS k
Author(s) -
ROONEY M.
Publication year - 1996
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/(sici)1097-0207(19961115)39:21<3663::aid-nme18>3.0.co;2-e
Subject(s) - tridiagonal matrix , matrix (chemical analysis) , mathematics , algebraic equation , algebraic number , band matrix , tridiagonal matrix algorithm , mathematical analysis , materials science , symmetric matrix , physics , square matrix , composite material , quantum mechanics , eigenvalues and eigenvectors , nonlinear system
The traditional tridiagonal matrix approximating the one‐dimensional heat equation is ill‐conditioned when heat conductivity changes radically. An algebraic reformulation of the tridiagonal produces a well‐conditioned matrix. Additional variables are rates q =− ku x at interfaces between radical changes in k . A reduced matrix amounts to a coarse approximation.