Araştırma Makalesi

Numerical Solution of Time and Space Fractional Burger's Equation with Finite Difference Method

Cilt: 4 Sayı: 2 31 Ağustos 2019
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Numerical Solution of Time and Space Fractional Burger's Equation with Finite Difference Method

Öz

In this study, fractional Burger’s Equation, which has Dirichlet Boundary Conditions, is solved with the Finite Difference Method. Fractional Burger Equation is found by S. Momani, which is made with changing time and space terms with fractional terms. This equation is solved with the finite difference method and analysis of this scheme is discussed with examples. Stability and Uniqueness are discussed with using matrix method. We compare analytical and numerical solutions with error analysis of them.

Anahtar Kelimeler

Kaynakça

  1. [1] Zhang, Y., “A finite difference method for fractional partial differential equation”, Applied Mathematics and Computation 215 (2009) : 524-529.
  2. [2] Podlubny, I., “Fractional differential equation”, V198 of Mathematics in Science and Engineering, Academic Press, San Diego, (1999).
  3. [3] Zhang, P.G., Wang, J.P., “A predictor–corrector compact finite difference scheme for Burgers’ equation”, Applied Mathematics and Computation 219 (2012) : 892-898.
  4. [4] Varöglu, E., Liam Finn, W.D., “Space-time finite elements incorporating characteristics for the burgers’ equation”, Int. J. Numer. Methods Eng. 16 (1980) : 171–184.
  5. [5] Kutluay, S., Bahadir, A.R., Özdes, A., “Numerical solution of one-dimensional burgers equation: explicit and exact-explicit finite difference methods”, J. Comput. Appl. Math 103 (1999) : 251–261.
  6. [6] Pandey, K., Verma, L.,. Verma, A.K, “On a finite difference scheme for burgers’ equation”, Appl. Math. Comput 215 (2009) : 2206-2214.
  7. [7] Liao, W., “An implicit fourth-order compact finite difference scheme for one-dimensional burgers’ equation”, Appl. Math. Comput 206 (2008) : 755-764.
  8. [8] Saria, M., Gürarslanb, G., “A sixth-order compact finite difference scheme to the numerical solutions of burgers’ equation”, Appl. Math. Comput 208 (2009) : 475-483.

Ayrıntılar

Birincil Dil

İngilizce

Konular

Matematik

Bölüm

Araştırma Makalesi

Yayımlanma Tarihi

31 Ağustos 2019

Gönderilme Tarihi

12 Temmuz 2019

Kabul Tarihi

23 Ağustos 2019

Yayımlandığı Sayı

Yıl 2019 Cilt: 4 Sayı: 2

Kaynak Göster

APA
Kurulay, M., & Şentürk, İ. (2019). Numerical Solution of Time and Space Fractional Burger’s Equation with Finite Difference Method. Journal of Engineering Technology and Applied Sciences, 4(2), 71-83. https://doi.org/10.30931/jetas.614506
AMA
1.Kurulay M, Şentürk İ. Numerical Solution of Time and Space Fractional Burger’s Equation with Finite Difference Method. Journal of Engineering Technology and Applied Sciences. 2019;4(2):71-83. doi:10.30931/jetas.614506
Chicago
Kurulay, Muhammet, ve İbrahim Şentürk. 2019. “Numerical Solution of Time and Space Fractional Burger’s Equation with Finite Difference Method”. Journal of Engineering Technology and Applied Sciences 4 (2): 71-83. https://doi.org/10.30931/jetas.614506.
EndNote
Kurulay M, Şentürk İ (01 Ağustos 2019) Numerical Solution of Time and Space Fractional Burger’s Equation with Finite Difference Method. Journal of Engineering Technology and Applied Sciences 4 2 71–83.
IEEE
[1]M. Kurulay ve İ. Şentürk, “Numerical Solution of Time and Space Fractional Burger’s Equation with Finite Difference Method”, Journal of Engineering Technology and Applied Sciences, c. 4, sy 2, ss. 71–83, Ağu. 2019, doi: 10.30931/jetas.614506.
ISNAD
Kurulay, Muhammet - Şentürk, İbrahim. “Numerical Solution of Time and Space Fractional Burger’s Equation with Finite Difference Method”. Journal of Engineering Technology and Applied Sciences 4/2 (01 Ağustos 2019): 71-83. https://doi.org/10.30931/jetas.614506.
JAMA
1.Kurulay M, Şentürk İ. Numerical Solution of Time and Space Fractional Burger’s Equation with Finite Difference Method. Journal of Engineering Technology and Applied Sciences. 2019;4:71–83.
MLA
Kurulay, Muhammet, ve İbrahim Şentürk. “Numerical Solution of Time and Space Fractional Burger’s Equation with Finite Difference Method”. Journal of Engineering Technology and Applied Sciences, c. 4, sy 2, Ağustos 2019, ss. 71-83, doi:10.30931/jetas.614506.
Vancouver
1.Muhammet Kurulay, İbrahim Şentürk. Numerical Solution of Time and Space Fractional Burger’s Equation with Finite Difference Method. Journal of Engineering Technology and Applied Sciences. 01 Ağustos 2019;4(2):71-83. doi:10.30931/jetas.614506