New homotopy analysis transform method for solving the discontinued problems arising in nanotechnology

doi:10.1088/1674-1056/22/11/110201

中国物理B ›› 2013, Vol. 22 ›› Issue (11): 110201-110201.doi: 10.1088/1674-1056/22/11/110201

• GENERAL • 下一篇

New homotopy analysis transform method for solving the discontinued problems arising in nanotechnology

M. M. Khader^{a b}, Sunil Kumar^c, S. Abbasbandy^d

a Department of Mathematics and Statistics, College of Science, Al-Imam Mohammed Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia;
b Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt;
c Department of Mathematics, National Institute of Technology, Jamshedpur, India;
d Department of Mathematics, Imam Khomeini International University, Ghazvin, Iran

收稿日期:2013-01-14 修回日期:2013-06-27 出版日期:2013-09-28 发布日期:2013-09-28

New homotopy analysis transform method for solving the discontinued problems arising in nanotechnology

M. M. Khader^{a b}, Sunil Kumar^c, S. Abbasbandy^d

a Department of Mathematics and Statistics, College of Science, Al-Imam Mohammed Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia;
b Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt;
c Department of Mathematics, National Institute of Technology, Jamshedpur, India;
d Department of Mathematics, Imam Khomeini International University, Ghazvin, Iran

Received:2013-01-14 Revised:2013-06-27 Online:2013-09-28 Published:2013-09-28
Contact: M. M. Khader E-mail:mohamedmbd@yahoo.com

摘要/Abstract

摘要： We present a new reliable analytical study for solving the discontinued problems arising in nanotechnology. Such problems are presented as nonlinear differential–difference equations. The proposed method is based on the Laplace transform with the homotopy analysis method (HAM). This method is a powerful tool for solving a large amount of problems. This technique provides a series of functions which may converge to the exact solution of the problem. A good agreement between the obtained solution and some well-known results is obtained.

关键词: discretized mKdV lattice equation, nonlinear differential–difference equations, Laplace transform, homotopy analysis transform method

Abstract: We present a new reliable analytical study for solving the discontinued problems arising in nanotechnology. Such problems are presented as nonlinear differential–difference equations. The proposed method is based on the Laplace transform with the homotopy analysis method (HAM). This method is a powerful tool for solving a large amount of problems. This technique provides a series of functions which may converge to the exact solution of the problem. A good agreement between the obtained solution and some well-known results is obtained.

Key words: discretized mKdV lattice equation, nonlinear differential–difference equations, Laplace transform, homotopy analysis transform method

中图分类号: (Lie algebras of Lie groups)

02.20.Sv

47.15.-x (Laminar flows) 44.40.+a (Thermal radiation) 44.10.+i (Heat conduction)

M. M. Khader, Sunil Kumar, S. Abbasbandy. New homotopy analysis transform method for solving the discontinued problems arising in nanotechnology[J]. 中国物理B, 2013, 22(11): 110201-110201.

M. M. Khader, Sunil Kumar, S. Abbasbandy. New homotopy analysis transform method for solving the discontinued problems arising in nanotechnology[J]. Chin. Phys. B, 2013, 22(11): 110201-110201.

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New homotopy analysis transform method for solving the discontinued problems arising in nanotechnology

New homotopy analysis transform method for solving the discontinued problems arising in nanotechnology

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