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Zbl 1219.65119
Khan, Yasir; Wu, Qingbiao
Homotopy perturbation transform method for nonlinear equations using He's polynomials. (English)
[J] Comput. Math. Appl. 61, No. 8, 1963-1967 (2011). ISSN 0898-1221

Summary: A combined form of the Laplace transform method with the homotopy perturbation method is proposed to solve nonlinear equations. This method is called the homotopy perturbation transform method (HPTM). The nonlinear terms can be easily handled by the use of He's polynomials. The proposed scheme finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. The fact that the proposed technique solves nonlinear problems without using Adomian's polynomials can be considered as a clear advantage of this algorithm over the decomposition method.

MSC 2000:: *65M99 Numerical methods for IVP of PDE
35F25 Initial value problems for first order nonlinear PDE
35L60 First-order nonlinear hyperbolic equations

Keywords: Laplace transform method; homotopy perturbation method; nonlinear advection equations; He's polynomials

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