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

https://izlik.org/JA85GR99BS

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.