scholarly journals Solution of different geometries reflected reactors neutron diffusion equation using the homotopy perturbation method

2019 ◽  
Vol 12 ◽  
pp. 61-66 ◽  
Author(s):  
Mohammed Shqair
Keyword(s):  
Diffusion Equation ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Neutron Diffusion ◽  
Homotopy Perturbation ◽  
Neutron Diffusion Equation

scholarly journals Application of He's Homotopy Perturbation Method for Cauchy Problem of Ill-Posed Nonlinear Diffusion Equation

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Ali Zakeri ◽  
Azim Aminataei ◽  
Qodsiyeh Jannati
Keyword(s):  
Cauchy Problem ◽  
Diffusion Equation ◽  
Perturbation Method ◽  
Nonlinear Diffusion ◽  
Homotopy Perturbation Method ◽  
Finite Interval ◽  
Nonlinear Diffusion Equation ◽  
Third Order ◽  
Homotopy Perturbation ◽  
Ill Posed

We consider a Cauchy problem of unidimensional nonlinear diffusion equation on finite interval. This problem is ill-posed and its approximate solution is unstable. We apply the He's homotopy perturbation method (HPM) and obtain the third-order asymptotic expansion. We show that if the conductivity term in diffusion equation has a specified condition, the above solution can be estimated. Finally, a numerical experiment is provided to illustrate the method.

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