Almost analytic solutions and their tests of the horizontal diffusion equation for the movement of water in unsaturated soil

1997 ◽  
Vol 18 (7) ◽  
pp. 647-655 ◽  
Author(s):  
Li Hang ◽  
Liu Zhiqiang
Keyword(s):  
Diffusion Equation ◽  
Unsaturated Soil ◽  
Analytic Solutions ◽  
Horizontal Diffusion

Explicit Approximate Analytical Solution of the Horizontal Diffusion Equation

Soil Science ◽  
2015 ◽  
Vol 180 (2) ◽  
pp. 47-53 ◽  
Author(s):  
Christos Tzimopoulos ◽  
Chris Evangelides ◽  
George Arampatzis
Keyword(s):  
Analytical Solution ◽  
Diffusion Equation ◽  
Approximate Analytical Solution ◽  
Horizontal Diffusion

Solution of the Nonlinear Fractional Diffusion Equation with Absorbent Term and External Force Using Optimal Homotopy-Analysis Method

2012 ◽  
Vol 67 (3-4) ◽  
pp. 203-209 ◽  
Author(s):  
Kumar Vishal ◽  
Subir Das
Keyword(s):  
Diffusion Equation ◽  
External Force ◽  
Homotopy Analysis Method ◽  
Fractional Derivatives ◽  
Analytic Solutions ◽  
Control Parameters ◽  
Analysis Method ◽  
Optimal Homotopy Analysis Method ◽  
Homotopy Analysis ◽  
Convergence Control

In this article, the optimal homotopy-analysis method (HAM) is used to obtain approximate analytic solutions of the time-fractional nonlinear diffusion equation in the presence of an external force and an absorbent term. The fractional derivatives are considered in the Caputo sense to avoid nonzero derivative of constants. Unlike usual HAM this method contains at the most three convergence control parameters which determine the fast convergence of the solution through different choices of convergence control parameters. Effects of proper choice of parameters on the convergence of the approximate series solution by minimizing the averaged residual error for different particular cases are depicted through tables and graphs

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