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Application of the Adomian decomposition method for the Fokker–Planck equation

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Title: Application of the Adomian decomposition method for the Fokker–Planck equation
Authors: Tatari, Mehdi1 mehditatari@aut.ac.ir, Dehghan, Mehdi1 mdehghan@aut.ac.ir, Razzaghi, Mohsen1,2 razzaghi@math.msstate.edu
Source: Mathematical & Computer Modelling. Mar2007, Vol. 45 Issue 5/6, p639-650. 12p.
Subjects: Finite element method, Decomposition method, Operations research, System analysis
Abstract: Abstract: In this work we will discuss the solution of an initial value problem of parabolic type. The main objective is to propose an alternative method of solution, one not based on finite difference or finite element or spectral methods. The aim of the present paper is to investigate the application of the Adomian decomposition method for solving the Fokker–Planck equation and some similar equations. This method can successfully be applied to a large class of problems. The Adomian decomposition method needs less work in comparison with the traditional methods. This method decreases considerable volume of calculations. The decomposition procedure of Adomian will be obtained easily without linearizing the problem by implementing the decomposition method rather than the standard methods for the exact solutions. In this approach the solution is found in the form of a convergent series with easily computed components. In this work we are concerned with the application of the decomposition method for the linear and nonlinear Fokker–Planck equation. To give overview of methodology, we have presented several examples in one and two dimensional cases. [Copyright &y& Elsevier]
Copyright of Mathematical & Computer Modelling is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: <searchLink fieldCode="AR" term="%22Tatari%2C+Mehdi%22">Tatari, Mehdi</searchLink><relatesTo>1</relatesTo><i> mehditatari@aut.ac.ir</i><br /><searchLink fieldCode="AR" term="%22Dehghan%2C+Mehdi%22">Dehghan, Mehdi</searchLink><relatesTo>1</relatesTo><i> mdehghan@aut.ac.ir</i><br /><searchLink fieldCode="AR" term="%22Razzaghi%2C+Mohsen%22">Razzaghi, Mohsen</searchLink><relatesTo>1,2</relatesTo><i> razzaghi@math.msstate.edu</i>
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  Data: <searchLink fieldCode="JN" term="%22Mathematical+%26+Computer+Modelling%22">Mathematical & Computer Modelling</searchLink>. Mar2007, Vol. 45 Issue 5/6, p639-650. 12p.
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  Data: Abstract: In this work we will discuss the solution of an initial value problem of parabolic type. The main objective is to propose an alternative method of solution, one not based on finite difference or finite element or spectral methods. The aim of the present paper is to investigate the application of the Adomian decomposition method for solving the Fokker–Planck equation and some similar equations. This method can successfully be applied to a large class of problems. The Adomian decomposition method needs less work in comparison with the traditional methods. This method decreases considerable volume of calculations. The decomposition procedure of Adomian will be obtained easily without linearizing the problem by implementing the decomposition method rather than the standard methods for the exact solutions. In this approach the solution is found in the form of a convergent series with easily computed components. In this work we are concerned with the application of the decomposition method for the linear and nonlinear Fokker–Planck equation. To give overview of methodology, we have presented several examples in one and two dimensional cases. [Copyright &y& Elsevier]
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  Data: <i>Copyright of Mathematical & Computer Modelling is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – SubjectFull: Decomposition method
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      – SubjectFull: Operations research
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              Text: Mar2007
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