Approximate Analytical and Numerical Solutions for Time Fractional Generalized Nonlinear Huxley Equation

2021 ◽  
Vol 7 (4) ◽  
pp. 237-248
Keyword(s):  
Numerical Solutions ◽  
Analytical And Numerical Solutions ◽  
Huxley Equation

scholarly journals Evaluation of hillslope storage with variable width under temporally varied rainfall recharge

2021 ◽  
Author(s):  
Ping-Cheng Hsieh ◽  
Tzu-Ting Huang
Keyword(s):  
Groundwater Flow ◽  
Analytical Solutions ◽  
Water Conservation ◽  
Numerical Solutions ◽  
Integral Transform ◽  
Time Discretization ◽  
Third Order ◽  
Analytical And Numerical Solutions ◽  
Rainfall Recharge ◽  
Integral Transform Technique

Abstract. This study discussed water storage in aquifers of hillslopes under temporally varied rainfall recharge by employing a hillslope-storage equation to simulate groundwater flow. The hillslope width was assumed to vary exponentially to denote the following complex hillslope types: uniform, convergent, and divergent. Both analytical and numerical solutions were acquired for the storage equation with a recharge source. The analytical solution was obtained using an integral transform technique. The numerical solution was obtained using a finite difference method in which the upwind scheme was used for space derivatives and the third-order Runge–Kutta scheme was used for time discretization. The results revealed that hillslope type significantly influences the drains of hillslope storage. Drainage was the fastest for divergent hillslopes and the slowest for convergent hillslopes. The results obtained from analytical solutions require the tuning of a fitting parameter to better describe the groundwater flow. However, a gap existed between the analytical and numerical solutions under the same scenario owing to the different versions of the hillslope-storage equation. The study findings implied that numerical solutions are superior to analytical solutions for the nonlinear hillslope-storage equation, whereas the analytical solutions are better for the linearized hillslope-storage equation. The findings thus can benefit research on and have application in soil and water conservation.

Distributions of the potential and electric field of an electrode elliptic array used in tumor electrotherapy: Analytical and numerical solutions

2009 ◽  
Vol 79 (7) ◽  
pp. 2091-2105 ◽  
Author(s):  
Andrés Ramírez Aguilera ◽  
Luis Enrique Bergues Cabrales ◽  
Héctor Manuel Camué Ciria ◽  
Yudelmis Soler Pérez ◽  
Eduardo Roca Oria ◽  
...  
Keyword(s):  
Electric Field ◽  
Numerical Solutions ◽  
Analytical And Numerical Solutions
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