SavedAdd your journal

Journals / Conference Proceedings of Science and Technology / 2026 / Cilt: 3 Sayı: 1

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

Dilara Altan Koç(MUĞLA SITKI KOÇMAN ÜNİVERSİTESİ, FEN FAKÜLTESİ, MATEMATİK BÖLÜMÜ, MATEMATİK ANABİLİM DALI)
Yalçın Öztürk(MUĞLA SITKI KOÇMAN ÜNİVERSİTESİ, ULA ALİ KOÇMAN MESLEK YÜKSEKOKULU)0000-0002-4142-5633
Mustafa Gülsu(MUĞLA SITKI KOÇMAN ÜNİVERSİTESİ, FEN FAKÜLTESİ, MATEMATİK BÖLÜMÜ, MATEMATİK ANABİLİM DALI)
Pages
42–46
Publication Date
2020-12-15
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The graphics of errors for different mesh size are given.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we give a finite difference scheme to solve a special type of second order differential equations.
📊
Key Findings & Data:The approximate solutions are obtained by using Maple 13.
💡
Conclusion & Impact:The graphics of errors for different mesh size are given.
🔬Design:Konferans Bildirisi
📍Scope:Comprehensive Sample
⚙️Variables:Finite difference method · boundary value problem · Lagrange polynomial interpolation

Abstract

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.

🔖

Cite This Article

Koç, D. A., 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, Cilt: 3 Sayı: 1, 42–46. https://ajindex.com/articles/1648706

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (11)

  1. 1 J. F. Epperson, An Introduction to Numerical Methods and Analysis, Second Edition, John Wiley and Sons, (2013).
  2. 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. 3 G.D., Smith, Numerical Solution of Partial Differential Equations: Finite Difference Methods, Oxford University Press, (1985).
  4. 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. 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. 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. 7 J.F., Holt, Numerical solution of nonlinear two-point boundary problems by finite difference methods, Numerical Analysis, 7(6),(1964) 336-373.
  8. 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. 9 Z. Sun, X. Wu, A fully discrete difference scheme for a diffusion- wave system,Appl. Numer. Math., 56:(2017) 193-209.
  10. 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.
  11. 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.