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Rationalized Haar wavelet bases to approximate the solution of the first Painlev'e equations | ||
| Journal of Mathematical Modeling | ||
| مقاله 16، دوره 7، شماره 1، خرداد 2019، صفحه 107-116 اصل مقاله (258.86 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2018.11881.1214 | ||
| نویسندگان | ||
| Majid Erfanian* 1؛ Amin Mansoori2 | ||
| 1Department of Science, School of Mathematical Sciences, University of Zabol, Zabol, Iran | ||
| 2Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran | ||
| چکیده | ||
| In this article, using the properties of the rationalized Haar (RH) wavelets and the matrix operator, a method is presented for calculating the numerical approximation of the first Painlev'e equations solution. Also, an upper bound of the error is given and by applying the Banach fixed point theorem the convergence analysis of the method is stated. Furthermore, an algorithm to solve the first Painlev'e equation is proposed. Finally, the reported results are compared with some other methods to show the effectiveness of the proposed approach. | ||
| کلیدواژه‌ها | ||
| Wave equation؛ first Painlev'e equation؛ Volterra integral equation؛ RH wavelet | ||
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آمار تعداد مشاهده مقاله: 679 تعداد دریافت فایل اصل مقاله: 568 |
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