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A single cell high order scheme for the convection‐diffusion equation with variable coefficients
Author(s) -
Gupta Murli M.,
Manohar Ram P.,
Stephenson John W.
Publication year - 1984
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650040704
Subject(s) - stencil , mathematics , convection–diffusion equation , variable (mathematics) , truncation error , mathematical analysis , truncation (statistics) , diffusion , finite difference scheme , scheme (mathematics) , diffusion equation , central differencing scheme , finite difference method , finite difference , square (algebra) , finite difference coefficient , geometry , finite element method , physics , thermodynamics , mixed finite element method , statistics , computational science , economy , economics , service (business)
A new finite difference scheme for the convection‐diffusion equation with variable coefficients is proposed. The difference scheme is defined on a single square cell of size 2 h over a 9‐point stencil and has a truncation error of order h 4 . The resulting system of equations can be solved by iterative methods. Numerical results of some test problems are given.