An Efficient Approach for Fractional Harry Dym Equation by Using Sumudu Transform

An efficient approach based on homotopy perturbation method by using sumudu transform is proposed to solve nonlinear fractional Harry Dym equation. This method is called homotopy perturbation sumudu transform (HPSTM). Furthermore, the same problem is solved by Adomian decomposition method (ADM). The...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2013-01, Vol.2013 (2013), p.698-705-774
Main Authors: Kumar, Devendra, Singh, Jagdev, Kiliçman, Adem
Format: Article
Language:English
Subjects:
Accuracy
Algorithms
Cybernetics
Decomposition
Differential equations, Nonlinear
Laplace transforms
Mathematical research
Mathematics
Methods
Ordinary differential equations
Partial differential equations
Perturbation (Mathematics)
Studies
Transformations (Mathematics)
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Summary:An efficient approach based on homotopy perturbation method by using sumudu transform is proposed to solve nonlinear fractional Harry Dym equation. This method is called homotopy perturbation sumudu transform (HPSTM). Furthermore, 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 HPSTM show that the approach is easy to implement and computationally very attractive.
ISSN:1085-3375
1687-0409
DOI:10.1155/2013/608943