Research Article
BibTex RIS Cite

Zamansal-Kesirli Diferansiyel Fark Burger Denkleminin Sonlu Farklar Yöntemiyle Çözümü

Year 2019, , 258 - 262, 24.03.2019
https://doi.org/10.18185/erzifbed.449161

Abstract




Bu makalede zamansal-kesirli
diferansiyel fark Burger Denklemi
  üzerinde durulmuştur.
Bu denklemin sayısal çözümü için kompakt sonlu farklar metodu (
CFD) kullanılmıştır. Bu metoda göre, kompakt sonlu
fark yaklaşımı ile ilgili fonksiyonun bilinmeyen bir
 değerine yaklaşılmıştır.
Bir uygulama olarak, farklı iki kesir türevi (Riemann-Liouville ve Caputo) incelenmiştir.
Bu iki kesir türev tipi için farklı mertebelerde bulunan değerler
karşılaştırılmıştır. Sayısal sonuçlar, CFD yönteminin önerilen versiyonunun,
başlangıç koşulundan tüm verilerin yeterli yüksek doğrulukta elde edilmesini
sağladığını göstermektedir. 

References

  • Referans 1- Al-luhaibi, M. S., (2015) “New Iterative Method for Fractional Gas Dynamics and Coupled Burger’s Equations”. Hindawi Publishing Corporation The Scientific World Journal, Vol. 2015, Article ID 153124, 8 pages http://dx.doi.org/10.1155/2015/153124.Referans 2- Cui, M. (2009) “Compact finite difference method for the fractional diffusion equation”, Journal of Computational Physics, Vol. 228, pp. 7792-7804. Referans 3- Duarte, O. M. (2011) “Fractional-calculus-for-scientists-and-engineers”, Springer, USA. Referans 4-Hodzic-Zivanovic, S. and Jovanovic, B. S. (2017) “Additive Difference Scheme for Two Dimensional Fractional in Time Diffusion Equation”. Faculty of Sciences and Mathematics, University of Nis, Serbia. Filomat 31:2, pp. 217–226.Referans 5- Kilbas, A. A., Srivastava, H. M. and Trujillo, J. J. (2006) “Theory and Applications of Fractional Differential Equations”, Elsevier Science, USA.Referans 6- Li, C. and Zeng, F. (2015) “Numerical Methods for Fractional Calculus”, CRC Press, Boca Raton, USA.Referans 7- Miller, K. S. and Ross, B. (1993) “An-introduction-to-the-fractional-calculus-and-fractional-differential-equations”, Wiley-Interscience, USA.Referans 8- Mohan, J. J. and Deekshitulu, G. V. S. R. (2012) “Fractional Order Difference Equations”, International Journal of Differential Equations, Vol. 2012 Article ID 780619, 11 pages.Referans 9- Podlubny, I. (1988) “Fractional-Differential-Equations”, Elsevier, USA. Referans 10 - Podlubny, I. (1999) “Fractional Differential Equations”, Academic Press, San Diego, USA.Referans 11 - Rawashdeh, M. S. (2017) “A reliable method for the space-time fractional Burgers and time-fractionalCahn-Allen equations via the FRDTM”, Advances in Difference Equations, Vol. 2017:99.Referans 12 - Yokus, A. and Kaya, D. (2017) “Numerical and exact solutions for time fractional Burgers’ equation” J. Nonlinear Sci. Appl., Vol. 10, pp. 3419–3428.
Year 2019, , 258 - 262, 24.03.2019
https://doi.org/10.18185/erzifbed.449161

Abstract

References

  • Referans 1- Al-luhaibi, M. S., (2015) “New Iterative Method for Fractional Gas Dynamics and Coupled Burger’s Equations”. Hindawi Publishing Corporation The Scientific World Journal, Vol. 2015, Article ID 153124, 8 pages http://dx.doi.org/10.1155/2015/153124.Referans 2- Cui, M. (2009) “Compact finite difference method for the fractional diffusion equation”, Journal of Computational Physics, Vol. 228, pp. 7792-7804. Referans 3- Duarte, O. M. (2011) “Fractional-calculus-for-scientists-and-engineers”, Springer, USA. Referans 4-Hodzic-Zivanovic, S. and Jovanovic, B. S. (2017) “Additive Difference Scheme for Two Dimensional Fractional in Time Diffusion Equation”. Faculty of Sciences and Mathematics, University of Nis, Serbia. Filomat 31:2, pp. 217–226.Referans 5- Kilbas, A. A., Srivastava, H. M. and Trujillo, J. J. (2006) “Theory and Applications of Fractional Differential Equations”, Elsevier Science, USA.Referans 6- Li, C. and Zeng, F. (2015) “Numerical Methods for Fractional Calculus”, CRC Press, Boca Raton, USA.Referans 7- Miller, K. S. and Ross, B. (1993) “An-introduction-to-the-fractional-calculus-and-fractional-differential-equations”, Wiley-Interscience, USA.Referans 8- Mohan, J. J. and Deekshitulu, G. V. S. R. (2012) “Fractional Order Difference Equations”, International Journal of Differential Equations, Vol. 2012 Article ID 780619, 11 pages.Referans 9- Podlubny, I. (1988) “Fractional-Differential-Equations”, Elsevier, USA. Referans 10 - Podlubny, I. (1999) “Fractional Differential Equations”, Academic Press, San Diego, USA.Referans 11 - Rawashdeh, M. S. (2017) “A reliable method for the space-time fractional Burgers and time-fractionalCahn-Allen equations via the FRDTM”, Advances in Difference Equations, Vol. 2017:99.Referans 12 - Yokus, A. and Kaya, D. (2017) “Numerical and exact solutions for time fractional Burgers’ equation” J. Nonlinear Sci. Appl., Vol. 10, pp. 3419–3428.
There are 1 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Makaleler
Authors

Refet Polat 0000-0001-9761-8787

Publication Date March 24, 2019
Published in Issue Year 2019

Cite

APA Polat, R. (2019). Zamansal-Kesirli Diferansiyel Fark Burger Denkleminin Sonlu Farklar Yöntemiyle Çözümü. Erzincan University Journal of Science and Technology, 12(1), 258-262. https://doi.org/10.18185/erzifbed.449161