Fractional modelling arising in unidirectional propagation of long waves in dispersive media

Advances in Nonlinear Analysis

article

Sunil Kumar¹  Devendra Kumar²  Jagdev Singh³ 

[1] Department of Mathematics, National Institute of Technology;Department of Mathematics, Jagan Nath Gupta Institute of Engineering and Technology;Department of Mathematics, Jagan Nath University

关键词: Laplace transform method;    fractional order Burgers–Poisson equation;    hybrid algorithm;    approximate solution;    absolute error;    homotopy analysis transform method (HATM);   

DOI  :  10.1515/anona-2013-0033

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

The purpose of this paper is to propose a modified and simple algorithm for fractional modelling arising in unidirectional propagation of long wave in dispersive media by using the fractional homotopy analysis transform method (FHATM). This modified method is an innovative adjustment in the Laplace transform algorithm (LTA) and makes the calculation much simpler. The proposed technique solves the nonlinear problems without using Adomian polynomials and He’s polynomials which can be considered as a clear advantage of this new algorithm over decomposition and the homotopy perturbation transform method. This modified method yields an analytical and approximate solution in terms of a rapidly convergent series with easily computable terms. The numerical solutions obtained by the proposed algorithm indicate that the approach is easy to implement and computationally very attractive. Comparing our solution with the existing ones, we note an excellent agreement.

【 授权许可】

CC BY