Journal
SPRINGERPLUS
Volume 5, Issue -, Pages -Publisher
SPRINGER INT PUBL AG
DOI: 10.1186/s40064-016-1755-y
Keywords
Homotopy perturbation method; Nonlinear differential equation; Approximate solutions; Laplace transform; Laplace transform homotopy perturbation method; Variational calculus; Euler equation
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Funding
- National Council for Science and Technology of Mexico (CONACyT) [CB-2010-01, 157024]
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This article proposes the application of Laplace Transform-Homotopy Perturbation Method and some of its modifications in order to find analytical approximate solutions for the linear and nonlinear differential equations which arise from some variational problems. As case study we will solve four ordinary differential equations, and we will show that the proposed solutions have good accuracy, even we will obtain an exact solution. In the sequel, we will see that the square residual error for the approximate solutions, belongs to the interval [0.001918936920, 0.06334882582], which confirms the accuracy of the proposed methods, taking into account the complexity and difficulty of variational problems.
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