Correct Method of Analytical Solution of Multipoint Boundary Problems of Structural Analysis for Systems of Ordinary Differential Equations with Piecewise Constant Coefficients

2011 ◽  
Vol 250-253 ◽  
pp. 3652-3655 ◽  
Author(s):  
Pavel A. Akimov ◽  
Vladimir N. Sidorov
Keyword(s):  
Structural Analysis ◽  
Analytical Solution ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Computational Stability ◽  
Boundary Problems ◽  
Piecewise Constant ◽  
Multipoint Boundary ◽  
Correct Method ◽  
Constant Coefficients

This paper is devoted to correct method of analytical solution of multipoint boundary problems of structural analysis for systems of ordinary differential equations with piecewise constant coefficients. Its major peculiarities include universality, computer-oriented algorithm involving theory of distributions, computational stability, optimal conditionality of resultant systems and partial Jordan decomposition of matrix of coefficients, eliminating necessity of calculation of root vectors.

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.

Correct Wavelet-based Multilevel Discrete-Continual Methods for Local Solution of Boundary Problems of Structural Analysis

2013 ◽  
Vol 353-356 ◽  
pp. 3224-3227 ◽  
Author(s):  
Pavel A. Akimov ◽  
Marina L. Mozgaleva
Keyword(s):  
Structural Analysis ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Problem ◽  
Local Solution ◽  
Wavelet Basis ◽  
Boundary Problems ◽  
Piecewise Constant ◽  
Constant Coefficients ◽  
Operational Formulation

The distinctive paper is devoted to correct wavelet-based multilevel discrete-continual methods for local solution of boundary problems of structural analysis. Initial discrete-continual operational formulation of the considering problem and corresponding operational formulation with the use of wavelet basis are presented. Due to special algorithms of averaging within multigrid approach, reduction of the problem is provided. Resultant multipoint boundary problem of structural mechanics for system of ordinary differential equations with piecewise-constant coefficients is given.

Correct Multilevel Discrete-Continual Finite Element Method of Structural Analysis

2014 ◽  
Vol 1040 ◽  
pp. 664-669 ◽  
Author(s):  
Pavel A. Akimov ◽  
Alexandr M. Belostosky ◽  
Marina L. Mozgaleva ◽  
Mojtaba Aslami ◽  
Oleg A. Negrozov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Structural Analysis ◽  
Analytical Solutions ◽  
Computational Stability ◽  
Boundary Problems ◽  
Piecewise Constant ◽  
Computer Realization ◽  
Constant Coefficients ◽  
Element Method

The distinctive paper is devoted to correct multilevel 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 universality, computer-oriented algorithm involving theory of distributions, computational stability, optimal conditionality of resulting systems and partial Jordan decompositions of matrices of coefficients, eliminating necessity of calculation of root vectors.

Application of He’s Homotopy Perturbation Method to Stiff Systems of Ordinary Differential Equations

2008 ◽  
Vol 63 (1-2) ◽  
pp. 19-23 ◽  
Author(s):  
Mohammad Taghi Darvishi ◽  
Farzad Khani
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Perturbation Method ◽  
Ordinary Differential Equations ◽  
Homotopy Perturbation Method ◽  
Nonlinear Ordinary Differential Equations ◽  
Stiff Systems ◽  
Homotopy Perturbation ◽  
Linear And Nonlinear

We propose He’s homotopy perturbation method (HPM) to solve stiff systems of ordinary differential equations. This method is very simple to be implemented. HPM is employed to compute an approximation or analytical solution of the stiff systems of linear and nonlinear ordinary differential equations.

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