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A Finite Difference Method to Solve a Special Type of Second Order Differential Equations

Yıl 2020, Cilt: 3 Sayı: 1, 42 - 46, 15.12.2020

Dilara Altan Koç Yalçın Öztürk Mustafa Gülsu

Öz

In this study, we give a finite difference scheme to solve a special type of second order differential equations. Our numerical method based on finite difference relation which is obtained the Lagrange polynomial interpolations. By applying this method the equation is made discrete using appropriate finite difference approaches instead of derivatives. The approximate solutions are obtained by using Maple 13. Absolute errors are calculated. The results are analyzed with tables . The graphics of errors for different mesh size are given.

Anahtar Kelimeler

Finite difference method boundary value problem Lagrange polynomial interpolation

Kaynakça

  • 1 J. F. Epperson, An Introduction to Numerical Methods and Analysis, Second Edition, John Wiley and Sons, (2013).
  • 2 P., Amodio, I., Sgura, High-order finite difference schemes for the solution of second-order BVPs, Journal of Computational and Applied Mathematics, 176, (2005) 59-79.
  • 3 G.D., Smith, Numerical Solution of Partial Differential Equations: Finite Difference Methods, Oxford University Press, (1985).
  • 4 M.S.Rehman, M., Yaseen, T., Kamran, New Iterative Method for Solution of System of Linear Differential Equations, International Journal of Science and Research, 5(2), (2016) 1287-1289.
  • 5 B.P., Moghaddam, A numerical method based on finite-difference for solving fractional delay differential equations, Journal of Taibah University for Science, 7(3), (2013) 120-127.
  • 6 P.K., Pandey, Finite difference method for a second-order ordinary differential equation with a boundary condition of the third kind, , Computational Methods in Applied Mathematics ,10(1), (2010) 109-116.
  • 7 J.F., Holt, Numerical solution of nonlinear two-point boundary problems by finite difference methods, Numerical Analysis, 7(6),(1964) 336-373.
  • 8 M. M., Meerschaert, H. P. Scheffler, ve C., Tadjeran Quantum logics, C.A. Hooker (editor), Finite Difference methods for two-dimensional fractional dispersion equation, J. Comput. Phys. (2005) 211: 249-261.
  • 9 Z. Sun, X. Wu, A fully discrete difference scheme for a diffusion- wave system,Appl. Numer. Math., 56:(2017) 193-209.
  • 10 A.T. Balasim, M. A.Norhashidah, New group iterative schemes in the numerical solution of two-dimensional time fractional advection-diffusion equation, Cogent Math Stat, 4:(2017) 1412241.

Yıl 2020, Cilt: 3 Sayı: 1, 42 - 46, 15.12.2020

Dilara Altan Koç Yalçın Öztürk Mustafa Gülsu

Öz

Kaynakça

  • 1 J. F. Epperson, An Introduction to Numerical Methods and Analysis, Second Edition, John Wiley and Sons, (2013).
  • 2 P., Amodio, I., Sgura, High-order finite difference schemes for the solution of second-order BVPs, Journal of Computational and Applied Mathematics, 176, (2005) 59-79.
  • 3 G.D., Smith, Numerical Solution of Partial Differential Equations: Finite Difference Methods, Oxford University Press, (1985).
  • 4 M.S.Rehman, M., Yaseen, T., Kamran, New Iterative Method for Solution of System of Linear Differential Equations, International Journal of Science and Research, 5(2), (2016) 1287-1289.
  • 5 B.P., Moghaddam, A numerical method based on finite-difference for solving fractional delay differential equations, Journal of Taibah University for Science, 7(3), (2013) 120-127.
  • 6 P.K., Pandey, Finite difference method for a second-order ordinary differential equation with a boundary condition of the third kind, , Computational Methods in Applied Mathematics ,10(1), (2010) 109-116.
  • 7 J.F., Holt, Numerical solution of nonlinear two-point boundary problems by finite difference methods, Numerical Analysis, 7(6),(1964) 336-373.
  • 8 M. M., Meerschaert, H. P. Scheffler, ve C., Tadjeran Quantum logics, C.A. Hooker (editor), Finite Difference methods for two-dimensional fractional dispersion equation, J. Comput. Phys. (2005) 211: 249-261.
  • 9 Z. Sun, X. Wu, A fully discrete difference scheme for a diffusion- wave system,Appl. Numer. Math., 56:(2017) 193-209.
  • 10 A.T. Balasim, M. A.Norhashidah, New group iterative schemes in the numerical solution of two-dimensional time fractional advection-diffusion equation, Cogent Math Stat, 4:(2017) 1412241.
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Dilara Altan Koç

Yalçın Öztürk 0000-0002-4142-5633

Mustafa Gülsu

Yayımlanma Tarihi 15 Aralık 2020
Kabul Tarihi 2 Ekim 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 3 Sayı: 1

Kaynak Göster

APA Altan Koç, D., Öztürk, Y., & Gülsu, M. (2020). A Finite Difference Method to Solve a Special Type of Second Order Differential Equations. Conference Proceedings of Science and Technology, 3(1), 42-46.
AMA Altan Koç D, Öztürk Y, Gülsu M. A Finite Difference Method to Solve a Special Type of Second Order Differential Equations. Conference Proceedings of Science and Technology. Aralık 2020;3(1):42-46.
Chicago Altan Koç, Dilara, Yalçın Öztürk, ve Mustafa Gülsu. “A Finite Difference Method to Solve a Special Type of Second Order Differential Equations”. Conference Proceedings of Science and Technology 3, sy. 1 (Aralık 2020): 42-46.
EndNote Altan Koç D, Öztürk Y, Gülsu M (01 Aralık 2020) A Finite Difference Method to Solve a Special Type of Second Order Differential Equations. Conference Proceedings of Science and Technology 3 1 42–46.
IEEE D. Altan Koç, Y. Öztürk, ve M. Gülsu, “A Finite Difference Method to Solve a Special Type of Second Order Differential Equations”, Conference Proceedings of Science and Technology, c. 3, sy. 1, ss. 42–46, 2020.
ISNAD Altan Koç, Dilara vd. “A Finite Difference Method to Solve a Special Type of Second Order Differential Equations”. Conference Proceedings of Science and Technology 3/1 (Aralık 2020), 42-46.
JAMA Altan Koç D, Öztürk Y, Gülsu M. A Finite Difference Method to Solve a Special Type of Second Order Differential Equations. Conference Proceedings of Science and Technology. 2020;3:42–46.
MLA Altan Koç, Dilara vd. “A Finite Difference Method to Solve a Special Type of Second Order Differential Equations”. Conference Proceedings of Science and Technology, c. 3, sy. 1, 2020, ss. 42-46.
Vancouver Altan Koç D, Öztürk Y, Gülsu M. A Finite Difference Method to Solve a Special Type of Second Order Differential Equations. Conference Proceedings of Science and Technology. 2020;3(1):42-6.
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