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.
Keywords
Zamansal-kesirli burger denklemi Zamansal-kesirli diferansiyel-fark denklemi Kompakt sonlu farklar metodu.
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.
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.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Makaleler |
| Authors | |
| Publication Date | March 24, 2019 |
| Published in Issue | Year 2019 Volume: 12 Issue: 1 |