Laplace transform homotopy perturbation method for the approximation of variational problems

被引：10

作者：

Filobello-Nino, U. ^{[1
]}

Vazquez-Leal, H. ^{[1
]}

Rashidi, M. M. ^{[2
,3
]}

Sedighi, Hamid M. ^{[4
]}

Perez-Sesma, A. ^{[1
]}

Sandoval-Hernandez, M. ^{[5
]}

Sarmiento-Reyes, A. ^{[6
]}

Contreras-Hernandez, A. D. ^{[1
]}

Pereyra-Diaz, D. ^{[1
]}

Hoyos-Reyes, C. ^{[1
]}

Jimenez-Fernandez, V. M. ^{[1
]}

Huerta-Chua, J. ^{[7
]}

Castro-Gonzalez, F. ^{[1
]}

Laguna-Camacho, J. R. ^{[8
]}

机构：

[1] Univ Veracruzana, Fac Instrumentac Elect, Circuito Gonzalo Aguirre Beltran S-N, Xalapa 91000, Veracruz, Mexico

[2] Tongji Univ, Shanghai Key Lab Vehicle Aerodynam & Vehicle Ther, 4800 Cao An Rd, Shanghai 201804, Peoples R China

[3] ENN Tongji Clean Energy Inst Adv Studies, Shanghai, Peoples R China

[4] Shahid Chamran Univ, Dept Mech Engn, Ahvaz, Iran

[5] Univ Xalapa, Ciencia Cultura & Tecnol, Km 2 Carretera Xalapa Veracruz, Xalapa 91190, Veracruz, Mexico

[6] Natl Inst Astrophys Opt & Elect, Luis Enrique Erro 1, Puebla 72840, Mexico

[7] Univ Veracruzana, Fac Ingn Elect & Comunicac, Venustiano Carranza S-N, Poza Rica 93390, Veracruz, Mexico

[8] Univ Veracruzana, Fac Ingn Mecan Elect, Venustiano Carranza S-N, Poza Rica 93390, Veracruz, Mexico

来源：

SPRINGERPLUS | 2016年 / 5卷

关键词：

Homotopy perturbation method; Nonlinear differential equation; Approximate solutions; Laplace transform; Laplace transform homotopy perturbation method; Variational calculus; Euler equation; HEAT-TRANSFER; EQUATIONS; FLOW;

D O I：

10.1186/s40064-016-1755-y

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

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.

引用

页数：33

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