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On consistent finite difference formulae for ordinary differential equations
Author(s) -
Miller R. E.
Publication year - 1979
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.1620141012
Subject(s) - mathematics , boundary value problem , ordinary differential equation , mathematical analysis , differential equation , numerical partial differential equations , finite difference method , generalization , truncation error , numerical methods for ordinary differential equations , differential algebraic equation
Abstract This paper presents a finite difference method for two‐point boundary value problems described by fourth‐order ordinary differential equations which results in consistency of truncation errors. It is demonstrated that the order of the formulae used to approximate the boundary conditions must be higher than those used for similar derivative terms in the differential equation. A generalization of the method to differential equations of order n is discussed. The procedure is illustrated with a numerical example.