M. Deiaa, W. S. Elbeshbeeshy, I. El-Kalla, A. Elsaid
{"title":"THE SOLUTION OF ONE-PHASE STEFAN-LIKE PROBLEMS WITH A FORCING TERM BY MOVING TAYLOR SERIES","authors":"M. Deiaa, W. S. Elbeshbeeshy, I. El-Kalla, A. Elsaid","doi":"10.26480/msmk.01.2022.13.20","DOIUrl":null,"url":null,"abstract":"In this article, we construct an approximate series solution for the one-dimensional one-phase Stefan-like problems with a forcing term. An algorithm is proposed to represent the nonhomogeneous forcing term in a moving series form to incorporate it into the moving Taylor series method. Numerical examples are solved by the proposed algorithm and the results show that with a suitable number of terms in the utilized moving series, the approximate solution is in good agreement with the exact solution.","PeriodicalId":32521,"journal":{"name":"Matrix Science Mathematic","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Matrix Science Mathematic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26480/msmk.01.2022.13.20","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
In this article, we construct an approximate series solution for the one-dimensional one-phase Stefan-like problems with a forcing term. An algorithm is proposed to represent the nonhomogeneous forcing term in a moving series form to incorporate it into the moving Taylor series method. Numerical examples are solved by the proposed algorithm and the results show that with a suitable number of terms in the utilized moving series, the approximate solution is in good agreement with the exact solution.
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