期刊
SPRINGERPLUS
卷 5, 期 -, 页码 -出版社
SPRINGER INTERNATIONAL PUBLISHING AG
DOI: 10.1186/s40064-016-3487-4
关键词
Homotopy Perturbation Method (HPM); Laplace Transform (LT); Singular Initial value problems (IVPs); Lane-Emden type equations
资金
- Madhya Pradesh Council of Science and Technology (MPCST), Bhopal, Madhya Pradesh, India [1013/CST/R&D/PhyEnggSc/2015]
In this communication, we describe the Homotopy Perturbation Method with Laplace Transform (LT-HPM), which is used to solve the Lane-Emden type differential equations. It's very difficult to solve numerically the Lane-Emden types of the differential equation. Here we implemented this method for two linear homogeneous, two linear nonhomogeneous, and four nonlinear homogeneous Lane-Emden type differential equations and use their appropriate comparisons with exact solutions. In the current study, some examples are better than other existing methods with their nearer results in the form of power series. The Laplace transform used to accelerate the convergence of power series and the results are shown in the tables and graphs which have good agreement with the other existing method in the literature. The results show that LT-HPM is very effective and easy to implement.
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