scholarly journals PENYELESAIAN PERSAMAAN POISSON MENGGUNAKAN METODE HOMOTOPI PERTUBASI

2021 ◽  
Vol 13 (2) ◽  
pp. 105
Author(s):  
Mashuri Mashuri ◽  
Sulistiowati Nur Rahmi ◽  
Marwah Daud Wijayanti ◽  
Alviana Pratama Putri
Keyword(s):  
Exact Solution ◽  
Power Series ◽  
Poisson Equation ◽  
Homotopy Method ◽  
Initial Condition ◽  
The Poisson Equation

In this paper, we discuss the solution of the Poisson equation with some initial condition.  We use the homotopy pertubation method to get the solution.. The homotopy pertubation method is a combination of the homotopy method and the pertubation method. The solution of the equation is assumed to be in the form of a power series. The result is  by using the homotopy pertubation method for the diffution equation, the solution  is the same with the exact solution.  

scholarly journals Mass Distribution and Gravitational Potential of the Milky Way

2017 ◽  
Vol 26 (1) ◽  
pp. 1-6
Author(s):  
Slobodan Ninković
Keyword(s):  
Exact Solution ◽  
Poisson Equation ◽  
Mass Distribution ◽  
Milky Way ◽  
Dark Halo ◽  
New Formalism ◽  
The Poisson Equation ◽  
Cumulative Mass ◽  
First Time ◽  
Special Case

AbstractModels of mass distribution in the Milky Way are discussed where those yielding the potential analytically are preferred. It is noted that there are three main contributors to the Milky Way potential: bulge, disc and dark halo. In the case of the disc the Miyamoto-Nagai formula, as simple enough, has shown as a very good solution, but it has not been able to satisfy all requirements. Therefore, improvements, such as adding new terms or combining several Miyamoto-Nagai terms, have been attempted. Unlike the disc, in studying the bulge and dark halo the flattening is usually neglected, which offers the possibility of obtaining an exact solution of the Poisson equation. It is emphasized that the Hernquist formula, used very often for the bulge potential, is a special case of another formula and the properties of that formula are analysed. In the case of the dark halo, the slopes of its cumulative mass for the inner and outer parts are explained through a new formalism presented here for the first time.

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