Application of the optimal homotopy asymptotic method for the solution of the Korteweg–de Vries equation

The Optimal Homotopy Asymptotic Method (OHAM), a semi-analytic approximate technique for the treatment of time-dependent partial differential equations, has been used in this presentation. To see the effectiveness of the method, we consider Korteweg–de Vries (KdV) equation with different initial con...

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Published inMathematical and computer modelling Vol. 55; no. 3; pp. 1324 - 1333
Main Authors Idrees, M., Islam, S., Tirmizi, S.I.A., Haq, Sirajul
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.02.2012
Subjects
Asymptotic method
Initial value and time-dependent partial differential equations
Perturbation
Asymptotic method
Initial value and time-dependent partial differential equations
Perturbation
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Summary:The Optimal Homotopy Asymptotic Method (OHAM), a semi-analytic approximate technique for the treatment of time-dependent partial differential equations, has been used in this presentation. To see the effectiveness of the method, we consider Korteweg–de Vries (KdV) equation with different initial conditions. It provides us with a convenient way to control the convergence of approximate solutions. The obtained solutions show that the OHAM is more effective, simpler and easier than other methods. The results reveal that the method is explicit.
ISSN:0895-7177
1872-9479
DOI:10.1016/j.mcm.2011.10.010