{"title":"Klein-Gordon方程和sin - gordon方程的近似解","authors":"Majeed A. Yousif , Bewar A. Mahmood","doi":"10.1016/j.jaubas.2015.10.003","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we practiced relatively new, analytical method known as the variational homotopy perturbation method for solving Klein–Gordon and sine-Gordon equations. To present the present method’s effectiveness many examples are given. In this study, we compare numerical results with the exact solutions, the Adomian decomposition method (ADM), the variational iteration method (VIM), homotopy perturbation method (HPM), modified Adomian decomposition method (MADM), and differential transform method (DTM). The results reveal that the VHPM is very effective.</p></div>","PeriodicalId":17232,"journal":{"name":"Journal of the Association of Arab Universities for Basic and Applied Sciences","volume":"22 ","pages":"Pages 83-90"},"PeriodicalIF":0.0000,"publicationDate":"2017-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jaubas.2015.10.003","citationCount":"21","resultStr":"{\"title\":\"Approximate solutions for solving the Klein–Gordon and sine-Gordon equations\",\"authors\":\"Majeed A. Yousif , Bewar A. Mahmood\",\"doi\":\"10.1016/j.jaubas.2015.10.003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we practiced relatively new, analytical method known as the variational homotopy perturbation method for solving Klein–Gordon and sine-Gordon equations. To present the present method’s effectiveness many examples are given. In this study, we compare numerical results with the exact solutions, the Adomian decomposition method (ADM), the variational iteration method (VIM), homotopy perturbation method (HPM), modified Adomian decomposition method (MADM), and differential transform method (DTM). The results reveal that the VHPM is very effective.</p></div>\",\"PeriodicalId\":17232,\"journal\":{\"name\":\"Journal of the Association of Arab Universities for Basic and Applied Sciences\",\"volume\":\"22 \",\"pages\":\"Pages 83-90\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.jaubas.2015.10.003\",\"citationCount\":\"21\",\"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/S1815385215000310\",\"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/S1815385215000310","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Approximate solutions for solving the Klein–Gordon and sine-Gordon equations
In this paper, we practiced relatively new, analytical method known as the variational homotopy perturbation method for solving Klein–Gordon and sine-Gordon equations. To present the present method’s effectiveness many examples are given. In this study, we compare numerical results with the exact solutions, the Adomian decomposition method (ADM), the variational iteration method (VIM), homotopy perturbation method (HPM), modified Adomian decomposition method (MADM), and differential transform method (DTM). The results reveal that the VHPM is very effective.
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