Traveling wave solution by differential transformation method and reduced differential transformation method

Alexandria Engineering Journal

卷:55

Hamed Faghanpour Ganji¹  Seyed Abbas Mirhosseini-Amiri²  Davod Domiri Ganji³  Mohsen Jouya³ 

[1] Department of Aerospace Engineering, Amirkabir University of Technology (Tehran Polytechnic), Postal Code, Tehran, Iran;

[2] Department of Economic Sciences, University of Economic Sciences, Postal Code, Tehran, Iran;

[3] Department of Mechanical Engineering, Babol Noshirvani University of Technology, Postal Code, Babol, Iran;

关键词: Differential Transformation Method (DTM);    Reduced DTM;    Coupled Jaulent–Miodek equation;    Coupled Whitham–Broer–Kaup equation;   

DOI  :  10.1016/j.aej.2016.04.012

来源: DOAJ

【 摘 要 】

The present study further examines two recent semi-analytic methods, a reduced order of nonlinear differential transformation method (also called RDTM) and differential transformation method along with Pade approximation to discuss Jaulent–Miodek and coupled Whitham–Broer–Kaup equations. The basic ideas of these methods are briefly introduced and performance of the proposed methods for above mentioned equations is evaluated via comparing with exact solution. The results illustrate that the so-called DTM method, unlike RDTM, due to the presence of secular terms (similar to perturbation method), cannot be found practical for nonlinear partial differential equations (particularly in Acoustic and Wave propagation problems) even through utilizing Pade approximation; meanwhile, RDTM method, despite its simplicity and rapid convergence, assured a significant accuracy and great agreement, and thus it is fair to say that nonlinear problems together with Acoustic application which cannot be solved via Analytical methods, can be studied with reduced order of nonlinear differential transformation method.

【 授权许可】

Unknown