A semi‐analytical approach for fractional order Boussinesq equation in a gradient unconfined aquifers

2021 ◽  
Author(s):  
Saima Rashid ◽  
Khadija T. Kubra ◽  
H. Jafari ◽  
Sana Ullah Lehre
Keyword(s):  
Fractional Order ◽  
Analytical Approach ◽  
Boussinesq Equation ◽  
Unconfined Aquifers

scholarly journals Improved Solutions to the Linearized Boussinesq Equation with Temporally Varied Rainfall Recharge for a Sloping Aquifer

Water ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 826 ◽  
Author(s):  
Wu ◽  
Hsieh
Keyword(s):  
Groundwater Level ◽  
Boussinesq Equation ◽  
Integral Transformation ◽  
Transformation Method ◽  
Unconfined Aquifer ◽  
Convergence Criterion ◽  
Unconfined Aquifers ◽  
Linearized Boussinesq Equation ◽  
Sloping Aquifer ◽  
Rainfall Recharge

Sloping unconfined aquifers are commonly seen and well investigated in the literature. In this study, we propose a generalized integral transformation method to solve the linearized Boussinesq equation that governs the groundwater level in a sloping unconfined aquifer with an impermeable bottom. The groundwater level responses of this unconfined aquifer under temporally uniform recharge or nonuniform recharge events are discussed. After comparing with a numerical solution to the nonlinear Boussinesq equation, the proposed solution appears better than that proposed in a previous study. Besides, we found that the proposed solutions reached the convergence criterion much faster than the Laplace transform solution did. Moreover, the application of the proposed solution to temporally changing rainfall recharge is also proposed to improve on the previous quasi-steady state treatment of an unsteady recharge rate.

A Novel Approximate Analytical approach to solve the Boussinesq equation

2020 ◽  
Vol 33 (02) ◽  
Author(s):  
Dr. Amruta Daga Bhandari ◽  
◽  
Dr. Vikas H Pradhan ◽  
Keyword(s):  
Analytical Approach ◽  
Boussinesq Equation

Analytical Approach to (2+1)-Dimensional Boussinesq Equation and (3+1)-Dimensional Kadomtsev-Petviashvili Equation

2010 ◽  
Vol 65 (5) ◽  
pp. 411-417 ◽  
Author(s):  
Selin Sarıaydın ◽  
Ahmet Yıldırım
Keyword(s):  
Analytical Approach ◽  
Boussinesq Equation ◽  
Numerical Solutions ◽  
Perturbation Series ◽  
Solitary Wave Solutions ◽  
Convergent Power Series ◽  
Kp Equation ◽  
Homotopy Perturbation ◽  
Wave Solutions ◽  
Petviashvili Equation

In this paper, we studied the solitary wave solutions of the (2+1)-dimensional Boussinesq equation utt −uxx−uyy−(u2)xx−uxxxx = 0 and the (3+1)-dimensional Kadomtsev-Petviashvili (KP) equation uxt −6ux 2 +6uuxx −uxxxx −uyy −uzz = 0. By using this method, an explicit numerical solution is calculated in the form of a convergent power series with easily computable components. To illustrate the application of this method numerical results are derived by using the calculated components of the homotopy perturbation series. The numerical solutions are compared with the known analytical solutions. Results derived from our method are shown graphically.

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