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A computational approach for solving second-order nonlinear ordinary differential equations by means of Laguerre series

Year 2020, , 78 - 84, 13.03.2020
https://doi.org/10.17798/bitlisfen.576189

Abstract

In this work, a novel efficient numeric procedure for obtaining the approximate solution of a class of second-order nonlinear ordinary differential equations is presented which play a significant part in science and engineering branches. The technique is based on matrix equations and collocation points with truncated Laguerre series. The acquired approximate solutions subject to initial conditions are obtained in terms of Laguerre polynomials. Also, some examples together with error analysis techniques are acquired to demonstrate the efficacy of the present method, and the comparisons are made with current studies.

References

  • Fried I. 1979. Numerical Solution of Differential Equations, Academic Press, NY, 1079.
  • Gürbüz B., Sezer M. 2016. Laguerre polynomial solutions of a class of initial and boundary value problems arising in science and engineering fields, Acta Phys. Pol., A 129(1): 194-197. DOI:10.12693/APhysPolA.130.194.
  • Gürbüz B., Sezer M. 2017. A numerical solution of parabolic-type Volterra partial integro-differential equations by Laguerre collocation method, IJAPM 7(1): 49-58. DOI:10.17706/ijapm.2017.7.1.49-58A.
  • Jordan D. W., Smith P. 2007. Nonlinear Ordinary Differential Equations: An introduction for Scientists and Engineers, 4th Edition. Oxford University Press, NY.
  • King A. C., Billingham J., Otto S. R. 2003. Differential Equations: Linear, Nonlinear, Ordinary, Partial, Cambridge University Press, NY.

İkinci mertebeden lineer olmayan adi diferansiyel denklemlerin Laguerre serileri ile çözümü için hesaplamalı bir yaklaşım

Year 2020, , 78 - 84, 13.03.2020
https://doi.org/10.17798/bitlisfen.576189

Abstract

Bu çalışmada, fen ve mühendislik dallarında önemli bir rol oynayan ikinci dereceden doğrusal olmayan adi diferansiyel denklemlerin bir sınıfının yaklaşık çözümünü elde etmek için yeni ve etkili bir sayısal prosedür sunulmuştur. Teknik, matris denklemlerine ve kesilmiş Laguerre serileri ile sıralama noktalarına dayanmaktadır. Başlangıç koşullarına tabi olarak elde edilen yaklaşık çözümler, Laguerre polinomları tarafından elde edilir. Ayrıca, mevcut yöntemin etkinliğini ortaya koymak için hata analizi teknikleri ile birlikte bazı örnekler alınmış ve güncel çalışmalar ile karşılaştırmalar yapılmıştır.

References

  • Fried I. 1979. Numerical Solution of Differential Equations, Academic Press, NY, 1079.
  • Gürbüz B., Sezer M. 2016. Laguerre polynomial solutions of a class of initial and boundary value problems arising in science and engineering fields, Acta Phys. Pol., A 129(1): 194-197. DOI:10.12693/APhysPolA.130.194.
  • Gürbüz B., Sezer M. 2017. A numerical solution of parabolic-type Volterra partial integro-differential equations by Laguerre collocation method, IJAPM 7(1): 49-58. DOI:10.17706/ijapm.2017.7.1.49-58A.
  • Jordan D. W., Smith P. 2007. Nonlinear Ordinary Differential Equations: An introduction for Scientists and Engineers, 4th Edition. Oxford University Press, NY.
  • King A. C., Billingham J., Otto S. R. 2003. Differential Equations: Linear, Nonlinear, Ordinary, Partial, Cambridge University Press, NY.
There are 5 citations in total.

Details

Primary Language English
Journal Section Araştırma Makalesi
Authors

Burcu Gürbüz 0000-0002-4253-5877

Publication Date March 13, 2020
Submission Date June 11, 2019
Acceptance Date September 19, 2019
Published in Issue Year 2020

Cite

IEEE B. Gürbüz, “A computational approach for solving second-order nonlinear ordinary differential equations by means of Laguerre series”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 9, no. 1, pp. 78–84, 2020, doi: 10.17798/bitlisfen.576189.



Bitlis Eren Üniversitesi
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