A non-iterative shooting method for a non-linear diffusion problem using automatic differentiation

2004 ◽  
Vol 81 (5) ◽  
pp. 607-614
Author(s):  
Asai Asaithambi
Keyword(s):  
Shooting Method ◽  
Automatic Differentiation ◽  
Diffusion Problem ◽  
Linear Diffusion ◽  
Non Linear

scholarly journals Numerical resolution of an anisotropic non-linear diffusion problem

2015 ◽  
Vol 13 (1) ◽  
pp. 203-224 ◽  
Author(s):  
Stéphane Brull ◽  
Fabrice Deluzet ◽  
Alexandre Mouton
Keyword(s):  
Diffusion Problem ◽  
Linear Diffusion ◽  
Numerical Resolution ◽  
Non Linear

On subsolutions of a non-linear diffusion problem

1989 ◽  
Vol 11 (3) ◽  
pp. 409-416 ◽  
Author(s):  
W. Okrasiński ◽  
E. Meister
Keyword(s):  
Diffusion Problem ◽  
Linear Diffusion ◽  
Non Linear

Estimation of the non-linear diffusion coefficient with Marcov Chain Monte Carlo method based on the integral information

2017 ◽  
Vol 27 (3) ◽  
pp. 639-659 ◽  
Author(s):  
Zbigniew Bulinski ◽  
Helcio R.B. Orlande
Keyword(s):  
Monte Carlo ◽  
Diffusion Coefficient ◽  
Monte Carlo Method ◽  
Real Life ◽  
Diffusion Problem ◽  
Linear Diffusion ◽  
Content Type ◽  
Inverse Approach ◽  
Non Linear ◽  
Correlated Parameters

Purpose This paper aims to present development and application of the Bayesian inverse approach for retrieving parameters of non-linear diffusion coefficient based on the integral information. Design/methodology/approach The Bayes formula was used to construct posterior distribution of the unknown parameters of non-linear diffusion coefficient. The resulting aposteriori distribution of sought parameters was integrated using Markov Chain Monte Carlo method to obtain expected values of estimated diffusivity parameters as well as their confidence intervals. Unsteady non-linear diffusion equation was discretised with the Global Radial Basis Function Collocation method and solved in time using Crank–Nicholson technique. Findings A number of manufactured analytical solutions of the non-linear diffusion problem was used to verify accuracy of the developed inverse approach. Reasonably good agreement, even for highly correlated parameters, was obtained. Therefore, the technique was used to compute concentration dependent diffusion coefficient of water in paper. Originality/value An original inverse technique, which couples efficiently meshless solution of the diffusion problem with the Bayesian inverse methodology, is presented in the paper. This methodology was extensively verified and applied to the real-life problem.

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