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      Laplace transform homotopy perturbation method for the approximation of variational problems

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          Abstract

          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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          Most cited references 53

          • Record: found
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          Homotopy perturbation technique

           Ji-Huan He (1999)
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            Applications of Lie Groups to Differential Equations

             Peter Olver (1993)
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              A review of the decomposition method in applied mathematics

               G Adomian (1988)
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                Author and article information

                Contributors
                ufilobello@uv.mx
                hvazquez@uv.mx
                mmrashidi@tongji.edu.cn
                hmsedighi@gmail.com
                antperez@uv.mx
                tecuanapan@yahoo.com.mx
                jarocho@inaoep.mx
                anacontreras@uv.mx
                dpereyra@uv.mx
                choyos@uv.mx
                vicjimenez@uv.mx
                jeshuerta@uv.mx
                catrapato@hotmail.com
                jlaguna@uv.mx
                Journal
                Springerplus
                Springerplus
                SpringerPlus
                Springer International Publishing (Cham )
                2193-1801
                5 March 2016
                5 March 2016
                2016
                : 5
                Affiliations
                [ ]Facultad de Instrumentación Electrónica, Universidad Veracruzana, Circuito Gonzalo Aguirre Beltrán S/N, 91000 Xalapa, Veracruz Mexico
                [ ]Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems, Tongji University, 4800 Cao An Rd., Jiading, Shanghai, 201804 China
                [ ]ENN-Tongji Clean Energy Institute of Advanced Studies, Shanghai, China
                [ ]Department of Mechanical Engineering, Shahid Chamran University, Ahvaz, Iran
                [ ]Doctorado en Ciencia, Cultura y Tecnología, Universidad de Xalapa, Km 2 Carretera Xalapa-Veracruz, 91190 Xalapa, Veracruz Mexico
                [ ]National Institute for Astrophysics, Optics and Electronics, Luis Enrique Erro #1, Sta. María Tonantzintla, 72840 Puebla, Mexico
                [ ]Facultad de Ingeniería Electrónica y Comunicaciones, Universidad Veracruzana, Venustiano Carranza S/N, Col. Revolución, 93390 Poza Rica, Veracruz Mexico
                [ ]Facultad de Ingeniería Mecánica Eléctrica, Universidad Veracruzana, Venustiano Carranza S/N, Col. Revolución, 93390 Poza Rica, Veracruz Mexico
                Article
                1755
                10.1186/s40064-016-1755-y
                4779117
                27006884
                © Filobello-Nino et al. 2016

                Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License ( http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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                © The Author(s) 2016

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