An Exact Solution of the 2D Boussinesq Equation for the Three‐Point Method

Ground Water ◽  
2019 ◽  
Vol 57 (4) ◽  
pp. 507-509 ◽  
Author(s):  
Adam Szymański
Keyword(s):  
Exact Solution ◽  
Boussinesq Equation ◽  
Point Method ◽  
2D Boussinesq Equation

scholarly journals A Fourth Order Finite Difference Method for the Good Boussinesq Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
M. S. Ismail ◽  
Farida Mosally
Keyword(s):  
Exact Solution ◽  
Nonlinear System ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Fourth Order ◽  
Boussinesq Equation ◽  
First Order ◽  
System A ◽  
Accuracy And Stability ◽  
Linearization Techniques

The “good” Boussinesq equation is transformed into a first order differential system. A fourth order finite difference scheme is derived for this system. The resulting scheme is analyzed for accuracy and stability. Newton’s method and linearization techniques are used to solve the resulting nonlinear system. The exact solution and the conserved quantity are used to assess the accuracy and the efficiency of the derived method. Head-on and overtaking interactions of two solitons are also considered. The numerical results reveal the good performance of the derived method.

Approximate analytical solution for the one-dimensional nonlinear Boussinesq equation

2015 ◽  
Vol 25 (4) ◽  
pp. 831-840 ◽  
Author(s):  
Hossein Aminikhah
Keyword(s):  
Exact Solution ◽  
Laplace Transform ◽  
Arbitrary Function ◽  
Perturbation Methods ◽  
Boussinesq Equation ◽  
Approximate Solutions ◽  
Content Type ◽  
One Dimensional ◽  
Homotopy Perturbation ◽  
The One

Purpose – The purpose of this paper is to provide closed-form approximate solutions to the one-dimensional Boussinesq equation for a semi-infinite aquifer when the hydraulic head at the source is an arbitrary function of time. Combination of the Laplace transform and homotopy perturbation methods (LTHPM) are considered as an algorithm which converges rapidly to the exact solution of the nonlinear Boussinesq equation. Design/methodology/approach – The authors present the solution of nonlinear Boussinesq equation by combination of Laplace transform and new homotopy perturbation methods. An important property of the proposed method, which is clearly demonstrated in example, is that spectral accuracy is accessible in solving specific nonlinear nonlinear Boussinesq equation which has analytic solution functions. Findings – The authors proposed a combination of Laplace transform method and homotopy perturbation method to solve the one-dimensional Boussinesq equation. The results are found to be in excellent agreement. The results show that the LTNHPM is an effective mathematical tool which can play a very important role in nonlinear sciences. Originality/value – The authors provide closed-form approximate solutions to the one-dimensional Boussinesq equation for a semi-infinite aquifer when the hydraulic head at the source is an arbitrary function of time. In this work combination of Laplace transform and new homotopy perturbation methods (LTNHPM) are considered as an algorithm which converges rapidly to the exact solution of the nonlinear Boussinesq equation.

Soliton Soloution of Generalized 2D Boussinesq Equation with Quadratic and Cubic Nonlinearity

1989 ◽  
Vol 58 (3) ◽  
pp. 827-830 ◽  
Author(s):  
Michiaki Matsukawa ◽  
Shinsuke Watanabe ◽  
Hiroshi Tanaca
Keyword(s):  
Boussinesq Equation ◽  
Cubic Nonlinearity ◽  
2D Boussinesq Equation

Scanning Electron Microscopy of Dried and Acid Treated Shells of Difflugia

1973 ◽  
Vol 31 ◽  
pp. 448-449
Author(s):  
Barry S. Eckert ◽  
S. M. McGee-Russell
Keyword(s):  
Electron Microscopy ◽  
Scanning Electron Microscopy ◽  
Critical Point ◽  
Point Method ◽  
External Structure ◽  
Cell Locomotion ◽  
Single Opening ◽  
Scanning Electron

Difflugia lobostoma is a shelled amoeba. The shell is an external structure of considerable mass which presents the animal with special restrictions in cell locomotion which are met by the development of active pseudopodial lobopodia containing, apparently, an organized system of thick and thin microfilaments (Eckert and McGee-Russell, 1972). The shell is constructed of sand grains picked up from the environment, and cemented into place with a secretion. There is a single opening through which lobopods extend. The organization of the shell was studied by scanning electron microscopy (SEM).Intact shells or animals with shells were dried by the critical point method of Anderson (1966) or air dried, after primary fixation in glutaraldehyde.

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