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The efficiency of transmission‐line matrix modelling—a rigorous viewpoint
Author(s) -
Enders Peter,
De Cogan Donard
Publication year - 1993
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/jnm.1660060204
Subject(s) - scalar (mathematics) , mathematics , matrix (chemical analysis) , diffusion , homogeneous , transmission line , diffusion equation , basis (linear algebra) , line (geometry) , telegrapher's equations , mathematical analysis , computer science , physics , geometry , telecommunications , materials science , economy , combinatorics , economics , composite material , service (business) , thermodynamics
The difference equations of the scalar linear transmission‐line matrix (TLM) routine as introduced by Johns for numerically solving the diffusion equation are shown to be isomorphic to Goldstein's correlated random walk model of diffusion. For the infinite homogeneous bar their exact solution is derived algebraically and given in the form of Jacobi polynomials. This puts the TLM algorithm on a sounder mathematical and physical basis. The accuracy in solving the diffusion equation is investigated in general form and thus its astonishing efficiency explained. Several other basic questions of this numerical technique are also discussed.