Homotopy Perturbation Method for Fractional Gas Dynamics Equation Using Sumudu Transform. (13th February 2013)

• Record Type: Journal Article
• Authors: Singh, Jagdev; Kumar, Devendra; Kılıçman, A.
• Other Names: Xu Lan Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-02-13
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/934060
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : A user friendly algorithm based on new homotopy perturbation Sumudu transform method (HPSTM) is proposed to solve nonlinear fractional gas dynamics equation. The fractional derivative is considered in the Caputo sense. Further, the same problem is solved by Adomian decomposition method (ADM). The results obtained by the two methods are in agreement and hence this technique may be considered an alternative and efficient method for finding approximate solutions of both linear and nonlinear fractional differential equations. The HPSTM is a combined form of Sumudu transform, homotopy perturbation method, and He's polynomials. The nonlinear terms can be easily handled by the use of He's polynomials. The numerical solutions obtained by the proposed method show that the approach is easy to implement and computationally very attractive.