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An attenuation‐free upwind difference formula for analogue computation of charge flow in semiconductors
Author(s) -
O'Carroll M. J.,
Foster K.,
McKay C. M.
Publication year - 1977
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.1620110305
Subject(s) - attenuation , computation , mathematics , ordinary differential equation , upwind scheme , mathematical analysis , flow (mathematics) , dispersion (optics) , differential equation , geometry , physics , discretization , algorithm , optics
The first order partial differential equations of charge flow are commonly differenced in the space co‐ordinate, with a view to analogue computation of the resulting ordinary differential equations in time. Defects of orthodox difference formulae are identified. In particular: (a) reversed waves and stability problems arise from central differences and (b) first order errors and a ‘pseudo‐viscous’ dispersion effect with accompanying false attenuation results from upwind differences. These difficulties are particularly serious in view of the coarse differencing required for practical analogue computation. A much superior formula is presented which is entirely free of attenuation and is easily implemented. Various other desirable features are reported.