Extended cubic B-spline solution of the advection-diffusion equation

2014 ◽  
Vol 19 (4) ◽  
pp. 929-934 ◽  
Author(s):  
Dursun Irk ◽  
İdris Dağ ◽  
Mustafa Tombul
Keyword(s):  
Diffusion Equation ◽  
B Spline ◽  
Advection Diffusion Equation ◽  
Advection Diffusion

Galerkin-least square B-spline approach toward advection–diffusion equation

2015 ◽  
Vol 261 ◽  
pp. 128-140 ◽  
Author(s):  
S. Dhawan ◽  
Samir Kumar Bhowmik ◽  
Sheo Kumar
Keyword(s):  
Diffusion Equation ◽  
Least Square ◽  
B Spline ◽  
Advection Diffusion Equation ◽  
Advection Diffusion

Numerical solution of highly non-linear fractional order reaction advection diffusion equation using the cubic B-spline collocation method

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Kushal Dhar Dwivedi ◽  
Subir Das ◽  
Rajeev ◽  
Dumitru Baleanu
Keyword(s):  
Diffusion Equation ◽  
Collocation Method ◽  
Fractional Order ◽  
Order Reaction ◽  
Spline Collocation ◽  
Diffusion Term ◽  
B Spline ◽  
Spline Collocation Method ◽  
Advection Diffusion Equation ◽  
Advection Diffusion

Abstract In this article, the approximate solution of the fractional-order reaction advection-diffusion equation with the prescribed initial and boundary conditions is found with the help of a cubic B-spline collocation method, which is unconditionally stable and convergent. The accuracy of the scheme is validated by applying the method on four existing problems having analytical solutions and through the evaluation of the absolute errors between numerical results and the exact solutions for different particular cases. Applying the proposed method on the last two numerical problems, it is shown that the method performs better than the existing methods even for very less number of spatial and temporal discretizations. The main contribution of the article is to develop an efficient method to solve the proposed fractional order nonlinear problem and to find the effect on solute concentration graphically due to increase in the non-linearity in the diffusion term for different particular values of parameters.

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