Analysis and parameter identification of bilinear systems via shifted Legendre polynomials

1986 ◽  
Vol 44 (2) ◽  
pp. 351-362 ◽  
Author(s):  
CHYI HWANG ◽  
MUH-YANG CHEN
Keyword(s):  
Parameter Identification ◽  
Legendre Polynomials ◽  
Bilinear Systems ◽  
Shifted Legendre Polynomials

The Application of Shifted Legendre Polynomials to Time-Delay Systems and Parameter Identification

1985 ◽  
Vol 107 (1) ◽  
pp. 79-85 ◽  
Author(s):  
Rong-Yeu Chang ◽  
Maw-Ling Wang
Keyword(s):  
Time Delay ◽  
Parameter Identification ◽  
Legendre Polynomials ◽  
Linear Time ◽  
Delay System ◽  
Delay Systems ◽  
Time Interval ◽  
Algebraic Equations ◽  
Shifted Legendre Polynomials ◽  
Expansion Coefficients

A linear time-delay state equation is solved by the proposed shifted Legendre polynomials method. The parameter identification of such a system with time delay is also studied. The system is partitioned into several time intervals. Within a certain time interval, the state and control functions are assumed to be expressed by the shifted Legendre polynomials series. Time-delay differential equations are transformed into a series of algebraic equations of expansion coefficients. An effective algorithm is proposed to solve the time-delay system problem and to estimate the system parameters. Only a small number of leading terms of expansion coefficients is enough to get accurate results. By using such an effective computational algorithm, the calculation procedures are greatly simplified. Thus much computer time is saved.

scholarly journals Numerical study of heat transfer of a micropolar fluid through a porous medium with radiation

2018 ◽  
Vol 22 (1 Part B) ◽  
pp. 557-565 ◽  
Author(s):  
Fakhrodin Mohammadi ◽  
Mohammad Rashidi
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Collocation Method ◽  
Micropolar Fluid ◽  
Legendre Polynomials ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Shifted Legendre Polynomials ◽  
Non Linear

An efficient Spectral Collocation method based on the shifted Legendre polynomials was applied to get solution of heat transfer of a micropolar fluid through a porous medium with radiation. A similarity transformation is applied to convert the governing equations to a system of non-linear ordinary differential equations. Then, the shifted Legendre polynomials and their operational matrix of derivative are used for producing an approximate solution for this system of non-linear differential equations. The main advantage of the proposed method is that the need for guessing and correcting the initial values during the solution procedure is eliminated and a stable solution with good accuracy can be obtained by using the given boundary conditions in the problem. A very good agreement is observed between the obtained results by the proposed Spectral Collocation method and those of previously published ones.

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