Nonstandard finite difference schemes for linear and non-linear Fokker–Planck equations
The goal of this paper is to develop a nonstandard finite difference-based numerical technique for solving the one-dimensional linear and non-linear Fokker–Planck equations. Characteristics of the nonstandard finite difference method are presented to understand the development of the proposed method...
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| Veröffentlicht in: | Journal of engineering mathematics 2024-04, Vol.145 (1), Article 11 |
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| container_title | Journal of engineering mathematics |
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| creator | Neena, A. S. Clemence-Mkhope, Dominic P. Awasthi, Ashish |
| description | The goal of this paper is to develop a nonstandard finite difference-based numerical technique for solving the one-dimensional linear and non-linear Fokker–Planck equations. Characteristics of the nonstandard finite difference method are presented to understand the development of the proposed method. Conditions for the dynamic consistency of positivity and stability of the schemes are obtained. Numerical experiments have been carried out to demonstrate the competitiveness of the proposed methods in comparison to some existing standard methods. In support of the proposed method and analysis, the
l
2
and
l
∞
errors are also presented. |
| doi_str_mv | 10.1007/s10665-024-10346-2 |
| format | Article |
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l
2
and
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∞
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l
2
and
l
∞
errors are also presented.</description><subject>Applications of Mathematics</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Dynamic stability</subject><subject>Finite difference method</subject><subject>Fokker-Planck equation</subject><subject>Mathematical analysis</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematical Modeling and Industrial Mathematics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Theoretical and Applied Mechanics</subject><issn>0022-0833</issn><issn>1573-2703</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9kD1OAzEQhS0EEiFwASpL1Ibxz3p3SxQRQIqAAgoqy6zHsPnxJvamoOMO3JCTYNhIdFTzRvrem9Ej5JTDOQcoLxIHrQsGQjEOUmkm9siIF6VkogS5T0YAQjCopDwkRynNAaCulBiR57supN4GZ6Ojvg1tj9S13mPE0CBNzRuuMFHfRbpsA9pIM0tDF9hunXaLBcavj8-HpQ3NguJma_s2hx6TA2-XCU92c0yeplePkxs2u7--nVzOWJNf61mpVSMrrYTThXeNKl8qAETnsOCqtg64s-iUr4vGZqm8tKqWusoCawUox-RsyF3HbrPF1Jt5t40hnzSiLqUuNFR1psRANbFLKaI369iubHw3HMxPhWao0OQKzW-FRmSTHEwpw-EV41_0P65vcvt1-w</recordid><startdate>20240401</startdate><enddate>20240401</enddate><creator>Neena, A. S.</creator><creator>Clemence-Mkhope, Dominic P.</creator><creator>Awasthi, Ashish</creator><general>Springer Netherlands</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20240401</creationdate><title>Nonstandard finite difference schemes for linear and non-linear Fokker–Planck equations</title><author>Neena, A. S. ; Clemence-Mkhope, Dominic P. ; Awasthi, Ashish</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-764c38642d65fdc47b800eedde5149ad01daed4f95ca1da4f3a493684f3e940e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Applications of Mathematics</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Dynamic stability</topic><topic>Finite difference method</topic><topic>Fokker-Planck equation</topic><topic>Mathematical analysis</topic><topic>Mathematical and Computational Engineering</topic><topic>Mathematical Modeling and Industrial Mathematics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Theoretical and Applied Mechanics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Neena, A. S.</creatorcontrib><creatorcontrib>Clemence-Mkhope, Dominic P.</creatorcontrib><creatorcontrib>Awasthi, Ashish</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of engineering mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Neena, A. S.</au><au>Clemence-Mkhope, Dominic P.</au><au>Awasthi, Ashish</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Nonstandard finite difference schemes for linear and non-linear Fokker–Planck equations</atitle><jtitle>Journal of engineering mathematics</jtitle><stitle>J Eng Math</stitle><date>2024-04-01</date><risdate>2024</risdate><volume>145</volume><issue>1</issue><artnum>11</artnum><issn>0022-0833</issn><eissn>1573-2703</eissn><abstract>The goal of this paper is to develop a nonstandard finite difference-based numerical technique for solving the one-dimensional linear and non-linear Fokker–Planck equations. Characteristics of the nonstandard finite difference method are presented to understand the development of the proposed method. Conditions for the dynamic consistency of positivity and stability of the schemes are obtained. Numerical experiments have been carried out to demonstrate the competitiveness of the proposed methods in comparison to some existing standard methods. In support of the proposed method and analysis, the
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| subjects | Applications of Mathematics Computational Mathematics and Numerical Analysis Dynamic stability Finite difference method Fokker-Planck equation Mathematical analysis Mathematical and Computational Engineering Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Theoretical and Applied Mechanics |
| title | Nonstandard finite difference schemes for linear and non-linear Fokker–Planck equations |
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