APPLYING MULTIQUADRIC QUASI-INTERPOLATION TO SOLVE FOKKER-PLANCK EQUATION

The Fokker-Planck equation (FPE) arises in various fields in physics, chemistry, natural science. It is difficult to obtain analytical solutions, accordingly we resort to numerical methods. In this study, we present a meshfree method to solve FPE. It is based on the multiquadric quasi-interpolation...

Full description

Saved in:
Bibliographic Details
Published inTWMS journal of applied and engineering mathematics Vol. 13; no. 1; p. 152
Main Authors Rahimi, M, Adibi, H, Amirfakhrian, M
Format Journal Article
LanguageEnglish
Published Istanbul Turkic World Mathematical Society 01.01.2023
Elman Hasanoglu
Subjects
Equations
Exact solutions
Fokker-Planck equation
Interpolation
Mathematical analysis
Mathematical research
Mathematics
Methods
Numerical analysis
Numerical methods
Operators (mathematics)
Partial differential equations
Physics
Iran
Online AccessGet full text

Cover

More Information
Summary:The Fokker-Planck equation (FPE) arises in various fields in physics, chemistry, natural science. It is difficult to obtain analytical solutions, accordingly we resort to numerical methods. In this study, we present a meshfree method to solve FPE. It is based on the multiquadric quasi-interpolation (MQQI) operator [Please download the PDF to view the formula] and collocation technique. Here, [theta]-weighted finite difference scheme is used to discretize the temporal derivative. Then, the unknown function and its spatial derivatives are approximated by the multiquadric quasi-interpolation (MQQI) operator [Please download the PDF to view the formula]. Furthermore, the stability of the technique is investigated. This method is applied to some examples and the numerical results have been compared with the exact solutions and results of another method. Keywords: Fokker-Planck equation, multiquadric quasi-interpolation, [theta]-weighted finite difference method, collocation method, meshless method. AMS Subject Classification: 35Q84, 65M06.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2146-1147
2146-1147