A numerical approach based on ln-shifted Legendre polynomials for solving a fractional model of pollution

2017 ◽  
Vol 40 (18) ◽  
pp. 7356-7367 ◽  
Author(s):  
M. Jleli ◽  
M. Kirane ◽  
B. Samet
Keyword(s):  
Legendre Polynomials ◽  
Numerical Approach ◽  
Shifted Legendre Polynomials ◽  
Fractional Model

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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