A computational approach for solving second-order nonlinear ordinary differential equations by means of Laguerre series
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
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.
Details
| Primary Language | English |
|---|---|
| Journal Section | Araştırma Makalesi |
| Authors | |
| Publication Date | March 13, 2020 |
| Submission Date | June 11, 2019 |
| Acceptance Date | September 19, 2019 |
| Published in Issue | Year 2020 Volume: 9 Issue: 1 |
