We obtain solutions of the nonlinear Klein-Gordon equation using a novel operational method combined with the Adomian polynomial expansion of nonlinear functions. Our operational method does not use any integral transforms nor integration processes. We illustrate the application of our method by solving several examples and present numerical results that show the accuracy of the truncated series approximations to the solutions.
Abstract
We obtain solutions of the nonlinear Klein-Gordon equation using a novel operational method combined with the Adomian polynomial expansion of nonlinear functions. Our operational method does not use any integral transforms nor integration processes. We illustrate the application of our method by solving several examples and present numerical results that show the accuracy of the truncated series approximations to the solutions.
关键词
operational calculus /
partial differential equations /
nonlinear Klein-Gordon equation
{{custom_keyword}} /
Key words
operational calculus /
partial differential equations /
nonlinear Klein-Gordon equation
{{custom_keyword}} /
中图分类号：
02.30.Jr
02.30.Vv
{{custom_clc.code}}
({{custom_clc.text}})
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] E. Zauderer, Partial Differential Equations of Applied Mathematics, John Wiley & Sons, New Jersey (2006).
[2] Roger K. Dodd, J. Chris Eilbeck, John D. Gibbon, and Hedley C. Morris, Solitons and Nonlinear Wave Equations, Academic Press, Inc. Harcourt Brace Jovanovich, Publishers, London, New York (1982).
[3] R. Mittal and R. Bhatia, Int. J. Comput. Math. 92(2015) 2139.
[4] E. Deeba and S. Khuri, J. Comput. Phys. 124(1996) 442.
[5] D. Kumar, J. Singh, S. Kumar, et al., Alexandria Eng. J. 53(2014) 469.
[6] H. Dong-mei, Z. Guo-liang, and L. Zhang, Math. Probl. Eng. 2015 (2015) 1.
[7] Nakao Hayashi and Pavel I. Naumkin, Zeitschrift für Angewandte Mathematik und Physik (ZAMP) 59(2008) 1002.
[8] G. Bengochea and L. Verde-Star, Adv. Appl. Math. 47(2011) 330.
[9] J. Mikusiński, Operational Calculus, Pergamon Press, Oxford (1959).
[10] G. Bengochea, Appl. Math. Lett. 32 (2014) 48.
[11] G. Bengochea and L. Verde-Star, Math. Meth. Appl. Sci. 38(2015) 4630.
[12] G. Bengochea, Appl. Math. Comput. 232(2014) 424.
[13] G. Bengochea, Fractional Calculus and Applied Analysis 18(2015) 1201.
[14] G. Bengochea and M. Ortigueira, J. Appl. Analysis 22(2016) 131.
[15] G. Bengochea and M. D. Ortigueira, Int. J. Dyn. Control 5 (2017) 61.
[16] G. Adomian, Math. Comput. Model. 13(1990) 17.
[17] Y. Cherruault and G. Adomian, Math. Comput. Model. 18(1993) 103.
[18] G. Guellal and Y. Cherruault, Int. J. Bio-Medical Comput. 36(1994) 223.
[19] M. M. Hosseini and H. Nasabzadeh, Appl. Math. Comput. 182(2006) 536.
[20] P. Guo, K. Liew, and P. Zhu, Appl. Math. Model. 39(2015) 2917.
[21] D. Kaya and Salah El-Sayed, Appl. Math. Comput. 156(2004) 341.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}
基金
Supported by Grant SEP-CONACYT 220603, the first author was supported by SEP-PRODEP through the project UAM-PTC-630, the third author was supported by Portuguese National Funds through the FCT Foundation for Science and Technology under the project PEst-UID/EEA/00066/2013
{{custom_fund}}
PDF(295 KB)
