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High‐order difference schemes for two‐dimensional elliptic equations
Author(s) -
Gupta Murli M.,
Manohar Ram P.,
Stephenson John W.
Publication year - 1985
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690010108
Subject(s) - stencil , mathematics , truncation error , truncation (statistics) , finite difference method , finite difference , elliptic curve , order (exchange) , square (algebra) , differential equation , approximation error , node (physics) , mathematical analysis , geometry , finance , engineering , economics , statistics , computational science , structural engineering
Abstract A high‐order finite‐difference approximation is proposed for numerical solution of linear or quasilinear elliptic differential equation. The approximation is defined on a square mesh stencil using nine node points and has a truncation error of order h 4 . Several test problems, including one modeling convection‐dominated flows, are solved using this and existing methods. The results clearly exhibit the superiority of the new approximation, in terms of both accuracy and computational efficiency.