Majeed Ahmed AL-Jawary , Ghassan Hasan Radhi , Jure Ravnik
{"title":"求解Fokker-Planck方程的半解析方法","authors":"Majeed Ahmed AL-Jawary , Ghassan Hasan Radhi , Jure Ravnik","doi":"10.1016/j.jaubas.2017.07.001","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, the linear and nonlinear Fokker-Planck equations (FPE) are solved by a semi-analytical iterative technique. This technique was proposed by Temimi and Ansari (TAM) in 2011. It is used to obtain the exact solutions for the 1D, 2D and 3D FPE. We solve several linear and nonlinear examples to show that the method is efficient and applicable. The results demonstrate that the presented method is very effective and reliable and does not require any restrictive assumptions for nonlinear terms. A symbolic manipulator Mathematica®10 was used to evaluate terms in the iterative process.</p></div>","PeriodicalId":17232,"journal":{"name":"Journal of the Association of Arab Universities for Basic and Applied Sciences","volume":"24 ","pages":"Pages 254-262"},"PeriodicalIF":0.0000,"publicationDate":"2017-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jaubas.2017.07.001","citationCount":"14","resultStr":"{\"title\":\"Semi-analytical method for solving Fokker-Planck’s equations\",\"authors\":\"Majeed Ahmed AL-Jawary , Ghassan Hasan Radhi , Jure Ravnik\",\"doi\":\"10.1016/j.jaubas.2017.07.001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, the linear and nonlinear Fokker-Planck equations (FPE) are solved by a semi-analytical iterative technique. This technique was proposed by Temimi and Ansari (TAM) in 2011. It is used to obtain the exact solutions for the 1D, 2D and 3D FPE. We solve several linear and nonlinear examples to show that the method is efficient and applicable. The results demonstrate that the presented method is very effective and reliable and does not require any restrictive assumptions for nonlinear terms. A symbolic manipulator Mathematica®10 was used to evaluate terms in the iterative process.</p></div>\",\"PeriodicalId\":17232,\"journal\":{\"name\":\"Journal of the Association of Arab Universities for Basic and Applied Sciences\",\"volume\":\"24 \",\"pages\":\"Pages 254-262\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.jaubas.2017.07.001\",\"citationCount\":\"14\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Association of Arab Universities for Basic and Applied Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1815385217300421\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Association of Arab Universities for Basic and Applied Sciences","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1815385217300421","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Semi-analytical method for solving Fokker-Planck’s equations
In this paper, the linear and nonlinear Fokker-Planck equations (FPE) are solved by a semi-analytical iterative technique. This technique was proposed by Temimi and Ansari (TAM) in 2011. It is used to obtain the exact solutions for the 1D, 2D and 3D FPE. We solve several linear and nonlinear examples to show that the method is efficient and applicable. The results demonstrate that the presented method is very effective and reliable and does not require any restrictive assumptions for nonlinear terms. A symbolic manipulator Mathematica®10 was used to evaluate terms in the iterative process.