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Kumar, Devendra; Singh, Jagdev; Kılıçman, A.

An efficient approach for fractional Harry Dym equation by using Sumudu transform. (English) Zbl 1275.65086

Abstr. Appl. Anal. 2013, Article ID 608943, 8 p. (2013).
Summary: An efficient approach based on the homotopy perturbation method by using the Sumudu transform is proposed to solve the nonlinear fractional Harry Dym equation. This method is called homotopy perturbation Sumudu transform (HPSTM). Furthermore, the same problem is solved by the 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 the Sumudu transform, the 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.

Cited in 13 Documents

MSC:

65N99 Numerical methods for partial differential equations, boundary value problems
35R11 Fractional partial differential equations
35A22 Transform methods (e.g., integral transforms) applied to PDEs

Keywords:

numerical examples; Laplace transform; homotopy perturbation method; Sumudu transform; nonlinear fractional Harry Dym equation; Adomian decomposition method
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\textit{D. Kumar} et al., Abstr. Appl. Anal. 2013, Article ID 608943, 8 p. (2013; Zbl 1275.65086)
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References:

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