A. Jameel, N. Anakira, A. Alomari, D. M. Alsharo, A. Saaban
{"title":"求解两点n阶模糊边值问题的半解析新方法","authors":"A. Jameel, N. Anakira, A. Alomari, D. M. Alsharo, A. Saaban","doi":"10.1504/IJMMNO.2019.096906","DOIUrl":null,"url":null,"abstract":"In this paper, a semi analytical algorithm, namely homotopy analysis method (HAM) is presented for the first time to obtain approximate analytical solutions of nth order two point fuzzy boundary value problems (TPFBVP) involving ordinary differential equations. This method allows for the solution of the TPFBVP to be calculated in the form of an infinite series with the components that can be easily calculated. The HAM utilises a convergence control parameter to control the convergence region of the infinite series solution. Numerical experiment is tested to highlight the important features of the HAM algorithm. Comparison of the HAM results and available exact solution reveal that this algorithm is effective and simple and for solving TPFBVP.","PeriodicalId":13553,"journal":{"name":"Int. J. Math. Model. Numer. Optimisation","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"New semi-analytical method for solving two point nth order fuzzy boundary value problem\",\"authors\":\"A. Jameel, N. Anakira, A. Alomari, D. M. Alsharo, A. Saaban\",\"doi\":\"10.1504/IJMMNO.2019.096906\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, a semi analytical algorithm, namely homotopy analysis method (HAM) is presented for the first time to obtain approximate analytical solutions of nth order two point fuzzy boundary value problems (TPFBVP) involving ordinary differential equations. This method allows for the solution of the TPFBVP to be calculated in the form of an infinite series with the components that can be easily calculated. The HAM utilises a convergence control parameter to control the convergence region of the infinite series solution. Numerical experiment is tested to highlight the important features of the HAM algorithm. Comparison of the HAM results and available exact solution reveal that this algorithm is effective and simple and for solving TPFBVP.\",\"PeriodicalId\":13553,\"journal\":{\"name\":\"Int. J. Math. Model. Numer. Optimisation\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Int. J. Math. Model. Numer. Optimisation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1504/IJMMNO.2019.096906\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Int. J. Math. Model. Numer. Optimisation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1504/IJMMNO.2019.096906","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
New semi-analytical method for solving two point nth order fuzzy boundary value problem
In this paper, a semi analytical algorithm, namely homotopy analysis method (HAM) is presented for the first time to obtain approximate analytical solutions of nth order two point fuzzy boundary value problems (TPFBVP) involving ordinary differential equations. This method allows for the solution of the TPFBVP to be calculated in the form of an infinite series with the components that can be easily calculated. The HAM utilises a convergence control parameter to control the convergence region of the infinite series solution. Numerical experiment is tested to highlight the important features of the HAM algorithm. Comparison of the HAM results and available exact solution reveal that this algorithm is effective and simple and for solving TPFBVP.
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