Mathematical Analysis and Convex Optimization آنالیز ریاضی و بهینه سازی محدب MACO Basic Sciences http://maco.lu.ac.ir 1 admin 2717-0624 2717-0624 8 10.29252/maco 14 8888 13 en jalali 1401 3 1 gregorian 2022 6 1 3 1 online 1 fulltext
en Application of Differential Transformation Method to the Dullin-Gottwald-Holm equation Applied Mathematics Applied Mathematics پژوهشي Research Article <pre> &lrm;Nonlinear problems in partial differential equations are open problems in many field of mathematics and engineering&lrm;. &lrm;So associated with the structure of the problems&lrm;, &lrm;many analytical and numerical methods are obtained&lrm;. &lrm;We show that the differential transformation method is an appropriate method for the Dullin-Gottwald-Holm equation&lrm; (DGH), &lrm;which is a nonlinear partial differential equation arise in many physical phenomenon&lrm;. &lrm;Hence in this paper&lrm;, &lrm;the differential transform method (DTM) is applied to the Dullin-Gottwald-Holm equation&lrm;. &lrm;We obtain the exact solutions of Dullin-Gottwald-Holm equation by using the DTM&lrm;. &lrm;In addition&lrm;, &lrm;we give some examples to illustrate the sufficiency of the method for solving such nonlinear partial differential equations&lrm;. &lrm;These results show that this technique is easy to apply and provide a suitable method for solving differential equations&lrm;. &lrm;To our best knowledge&lrm;, &lrm;the theorem presented in Section 2 has been not introduced previously&lrm;. &lrm;We presented and proved this new theorem which can be very effective for formulating the nonlinear forms of partial differential equations&lrm;.</pre> Dullin-Gottwald-Holm equation, Differential Transformation method, Spectral method. 23 35 http://maco.lu.ac.ir/browse.php?a_code=A-10-133-1&slc_lang=en&sid=1 Bahman Babayar-Razlighi babayar@qut.ac.ir `10031947532846001070` 10031947532846001070 Yes Department of Mathematics, Qom University of Technology, Qom, Iran Babak Soltanalizadeh babak.soltanalizadeh@uth.tmc.edu `10031947532846001071` 10031947532846001071 No Department of Biostatistics and Data Science, UT Health Science Center at Houston, Houston, TX, USA