Ahmad A. H. Mtawal, S. A. E. Muhammed, Ayiman A. Almabrok
{"title":"交替变分迭代法在求解时滞微分方程中的应用","authors":"Ahmad A. H. Mtawal, S. A. E. Muhammed, Ayiman A. Almabrok","doi":"10.5897/ijps2020.4879","DOIUrl":null,"url":null,"abstract":"In this paper, alternative variational iteration method (AVIM) is presented to solve linear and nonlinear delay differential equations (DDEs). A general lagrange multiplier is used to construct a correction functional. The proposed series solutions are found to converge to exact solution rapidly. The computation of three test examples of DDEs was presented to confirm the efficacy and validity of AVIM. The results obtained show that the AVIM is very simple and efficient. \n \n Key words: Alternative variational iteration method (AVIM), Lagrange multiplier, Delay differential equations (DDEs).","PeriodicalId":14294,"journal":{"name":"International Journal of Physical Sciences","volume":"6 1","pages":"112-119"},"PeriodicalIF":0.0000,"publicationDate":"2020-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Application of the alternative variational iteration method to solve delay differential equations\",\"authors\":\"Ahmad A. H. Mtawal, S. A. E. Muhammed, Ayiman A. Almabrok\",\"doi\":\"10.5897/ijps2020.4879\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, alternative variational iteration method (AVIM) is presented to solve linear and nonlinear delay differential equations (DDEs). A general lagrange multiplier is used to construct a correction functional. The proposed series solutions are found to converge to exact solution rapidly. The computation of three test examples of DDEs was presented to confirm the efficacy and validity of AVIM. The results obtained show that the AVIM is very simple and efficient. \\n \\n Key words: Alternative variational iteration method (AVIM), Lagrange multiplier, Delay differential equations (DDEs).\",\"PeriodicalId\":14294,\"journal\":{\"name\":\"International Journal of Physical Sciences\",\"volume\":\"6 1\",\"pages\":\"112-119\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-07-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Physical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5897/ijps2020.4879\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Physical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5897/ijps2020.4879","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Application of the alternative variational iteration method to solve delay differential equations
In this paper, alternative variational iteration method (AVIM) is presented to solve linear and nonlinear delay differential equations (DDEs). A general lagrange multiplier is used to construct a correction functional. The proposed series solutions are found to converge to exact solution rapidly. The computation of three test examples of DDEs was presented to confirm the efficacy and validity of AVIM. The results obtained show that the AVIM is very simple and efficient.
Key words: Alternative variational iteration method (AVIM), Lagrange multiplier, Delay differential equations (DDEs).