Finite Element Method for Ordinary Differential Equations

2000 ◽  
pp. 123-164 ◽  
Author(s):  
Gwynne A. Evans ◽  
Jonathan M. Blackledge ◽  
Peter D. Yardley
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Element Method

Correct Discrete-Continual Finite Element Method of Structural Analysis Based on Precise Analytical Solutions of Resulting Multipoint Boundary Problems for Systems of Ordinary Differential Equations

2012 ◽  
Vol 204-208 ◽  
pp. 4502-4505 ◽  
Author(s):  
Pavel A. Akimov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Structural Analysis ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Analytical Solutions ◽  
Computational Stability ◽  
Boundary Problems ◽  
Multipoint Boundary ◽  
Element Method

The distinctive paper is devoted to correct discrete-continual finite element method (DCFEM) of structural analysis based on precise analytical solutions of resulting multipoint boundary problems for systems of ordinary differential equations with piecewise-constant coefficients. Corresponding semianalytical (discrete-continual) formulations are contemporary mathematical models which currently becoming available for computer realization. Major peculiarities of DCFEM include uni-versality, computer-oriented algorithm involving theory of distributions, computational stability, optimal conditionality of resulting systems and partial Jordan decompositions of matrices of coeffi-cients, eliminating necessity of calculation of root vectors.

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