A General Solution of the Fokker-Planck Equation

Araujo, M. T.; Filho, Elso Drigo

doi:10.1007/s10955-011-0411-8

Cited by 14 publications

(20 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This solution involves the discrete levels of the problem and the other one uses a Gaussian distribution for all continuous states. Although the solution proposed in [8] agrees with the numerical results, the adopted approach can be improved upon.…”

Section: The Fokker-planck Equationmentioning

confidence: 72%

“…This paper presents an approximate analytical solution to the Fokker-Planck equation for partially confining potentials. The suggested solution corresponds to an adaptation of a previous proposal [8] from the same authors. Here, there is suggested the removal of the Gaussian function from the region of potential well, which permits a greater numerical accuracy of solution.…”

Section: Resultsmentioning

confidence: 99%

“…Another problem arises when one cannot get the solution of the corresponding Schrödinger equation (2.2). To get around this last problem, an approximate analytical solution composed of two parts was suggested in a previous paper [8]. This solution involves the discrete levels of the problem and the other one uses a Gaussian distribution for all continuous states.…”

Section: The Fokker-planck Equationmentioning

confidence: 99%

“…In section 2, there is a brief discussion of the Fokker-Planck equation and the approximate solution method is presented, with the changes suggested in relation to the previously proposed solution [8]. In sections 3 and 4, the proposed method is applied to two partially-confining potentials.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Approximate solution for Fokker-Planck equation

Araujo¹,

Filho²

2015

Condens. Matter Phys.

View full text Add to dashboard Cite

In this paper, an approximate solution to a specific class of the Fokker-Planck equation is proposed. The solution is based on the relationship between the Schrödinger type equation with a partially confining and symmetrical potential. To estimate the accuracy of the solution, a function error obtained from the original Fokker-Planck equation is suggested. Two examples, a truncated harmonic potential and non-harmonic polynomial, are analyzed using the proposed method. For the truncated harmonic potential, the system behavior as a function of temperature is also discussed.

show abstract

Section: The Fokker-planck Equationmentioning

confidence: 72%

Section: Resultsmentioning

confidence: 99%

Section: The Fokker-planck Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Approximate solution for Fokker-Planck equation

Araujo¹,

Filho²

2015

Condens. Matter Phys.

View full text Add to dashboard Cite

show abstract

“…We will show this in two examples: one with constant Schrödinger potential and another with Pöschl-Teller potential. The same example has been incorrectly treated in [10]. To avoid any confusion one has to note that the Pöschl-Teller potential is referred to as Rosen-Morse potential in [10].…”

Section: Introductionmentioning

confidence: 99%

How to solve Fokker-Planck equation treating mixed eigenvalue spectrum?

Brics¹,

Kaupužs²,

Mahnke³

2013

Condens. Matter Phys.

View full text Add to dashboard Cite

An analogy of the Fokker-Planck equation (FPE) with the Schrödinger equation allows us to use quantum mechanics technique to find the analytical solution of the FPE in a number of cases. However, previous studies have been limited to the Schrödinger potential with a discrete eigenvalue spectrum. Here, we will show how this approach can be also applied to a mixed eigenvalue spectrum with bounded and free states. We solve the FPE with boundaries located at x = ±L/2 and take the limit L → ∞, considering the examples with constant Schrödinger potential and with Pöschl-Teller potential. An oversimplified approach was proposed earlier by M.T. Araujo and E. Drigo Filho. A detailed investigation of the two examples shows that the correct solution, obtained in this paper, is consistent with the expected Fokker-Planck dynamics.

show abstract