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A finite element method for the general solution of ordinary differential equations
Author(s) -
Csendes Z. J.
Publication year - 1975
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.1620090305
Subject(s) - mathematics , exact differential equation , mathematical analysis , ordinary differential equation , homogeneous differential equation , finite element method , differential equation , matrix differential equation , universal differential equation , riccati equation , first order partial differential equation , integrating factor , matrix (chemical analysis) , collocation method , differential algebraic equation , physics , materials science , composite material , thermodynamics
A finite element method is developed by which it is possible to obtain the general solution of an ordinary differential equation directly. The procedure consists of approximating the differential equation with a rectangular matrix equation and of solving the latter equation by using generalized matrix inversion. It is shown in the paper that the homogeneous and inhomogeneous solutions of the two systems correspond and that the approximate solutions produced form the complete general solution of the original differential equation.