2008
DOI: 10.1007/s12190-008-0206-5
|View full text |Cite
|
Sign up to set email alerts
|

Approximate explicit solution of Camassa-Holm equation by He’s homotopy perturbation method

Abstract: In this paper, the homotopy perturbation method (HPM) is employed to solve Camassa-Holm equation. Approximate explicit solution is obtained. Comparing the approximate solution with its exact solution shows the applicability, accuracy and efficiency of HPM in solving nonlinear differential equations. It is predicted that HPM can be widely applied in applied mathematics and engineering problems.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1
1

Citation Types

2
9
0

Year Published

2011
2011
2019
2019

Publication Types

Select...
5

Relationship

0
5

Authors

Journals

citations
Cited by 5 publications
(11 citation statements)
references
References 31 publications
2
9
0
Order By: Relevance
“…Three test problems were performed to validate the precision and efficacy of the current method. Also, it was seen that the obtained results are a good agreement with the solution obtained by Zhang et al [11,28]. The main benefit of this approach is that linearization is not required for this method and therefore it reduces complex numerical computations significantly compared to the other existing methods such as the perturbation technique, DTM, and ADM. Small size computations over other techniques are the main advantages of the proposed method.…”
Section: Discussionsupporting
confidence: 82%
See 3 more Smart Citations
“…Three test problems were performed to validate the precision and efficacy of the current method. Also, it was seen that the obtained results are a good agreement with the solution obtained by Zhang et al [11,28]. The main benefit of this approach is that linearization is not required for this method and therefore it reduces complex numerical computations significantly compared to the other existing methods such as the perturbation technique, DTM, and ADM. Small size computations over other techniques are the main advantages of the proposed method.…”
Section: Discussionsupporting
confidence: 82%
“…One may see from Tables 2-4 that approximate solutions solved by FRDTM are quite close to the solutions solved by Zhang et al [11,28]. Zhang et al [11,28].…”
Section: Resultssupporting
confidence: 65%
See 2 more Smart Citations
“…In the homotopy technique (in topology), a homotopy is constructed with an embedding parameter which is considered as a "small parameter". Very recently HPM has been applied to a wide class of physical problems [10,12,13,17,22,23,24,25,30,33,34,39,40,41,42,43]. In these papers the parameters and variables are considered as crisp (exact).…”
Section: Introductionmentioning
confidence: 99%