{"title":"用vim和MHPM求解高阶积分微分方程","authors":"L. Dawood, A. Sharif, A. Hamoud","doi":"10.12732/ijam.v33i2.5","DOIUrl":null,"url":null,"abstract":"In this paper, the Variational Iteration Method (VIM) and Modified Homotopy Perturbation Method (MHPM) are applied to solve boundary value problems for higher-order Volterra integro-differential equations. The numerical results obtained with minimum amount of computation are compared with the exact solutions to show the efficiency of the methods. The results show that the variational iteration method is of high accuracy, more convenient and efficient for solving Volterra integro-differential equations. Finally, an example is included to demonstrate the validity and applicability of the proposed techniques. AMS Subject Classification: 45J05, 65K10, 65H20","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"2022 1","pages":"253"},"PeriodicalIF":0.0000,"publicationDate":"2020-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":"{\"title\":\"SOLVING HIGHER-ORDER INTEGRO DIFFERENTIAL EQUATIONS BY VIM AND MHPM\",\"authors\":\"L. Dawood, A. Sharif, A. Hamoud\",\"doi\":\"10.12732/ijam.v33i2.5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, the Variational Iteration Method (VIM) and Modified Homotopy Perturbation Method (MHPM) are applied to solve boundary value problems for higher-order Volterra integro-differential equations. The numerical results obtained with minimum amount of computation are compared with the exact solutions to show the efficiency of the methods. The results show that the variational iteration method is of high accuracy, more convenient and efficient for solving Volterra integro-differential equations. Finally, an example is included to demonstrate the validity and applicability of the proposed techniques. AMS Subject Classification: 45J05, 65K10, 65H20\",\"PeriodicalId\":14365,\"journal\":{\"name\":\"International journal of pure and applied mathematics\",\"volume\":\"2022 1\",\"pages\":\"253\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-05-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International journal of pure and applied mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12732/ijam.v33i2.5\",\"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 pure and applied mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12732/ijam.v33i2.5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
SOLVING HIGHER-ORDER INTEGRO DIFFERENTIAL EQUATIONS BY VIM AND MHPM
In this paper, the Variational Iteration Method (VIM) and Modified Homotopy Perturbation Method (MHPM) are applied to solve boundary value problems for higher-order Volterra integro-differential equations. The numerical results obtained with minimum amount of computation are compared with the exact solutions to show the efficiency of the methods. The results show that the variational iteration method is of high accuracy, more convenient and efficient for solving Volterra integro-differential equations. Finally, an example is included to demonstrate the validity and applicability of the proposed techniques. AMS Subject Classification: 45J05, 65K10, 65H20
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