Numerical comparison of nonstandard schemes for the Airy equation


  • Oluwaseye Adekanye Howard University
  • Talitha Washington Howard University





ODE, Nonstandard Finite Difference Scheme, Airy Equation


This paper considers the Airy ordinary differential equation (ODE) and different ways it can be discretized. We first consider a standard discretization using the central difference scheme. We then consider two difference schemes which were created using a nonstandard methodology. Finally, we compare the different schemes and how well they approximate solutions to the Airy ODE.


[1] L. Gr. Ixaru, M. Rizea, “Numerov method maximally adapted to the Schrodinger equationâ€, J. Comput. Phys., Vol. 73, (1987), 306-324.

[2] R. E. Mickens, “Nonstandard finite difference models of differential equationsâ€, World Scientific Publishing Co. Pte. Ltd., (1994).

[3] R. E. Mickens, “Nonstandard finite difference schemes for differential equationsâ€, Journal of Difference Equations and Applications, Vol. 8: 9, (2002), 823-847.

[4] R. E. Mickens, A. Smith, “Finite-difference models of ordinary differential equations: influence of denominator functionsâ€, Journal of the Franklin Institute Vol. 327, (1990), 143-149.

[5] R. E. Mickens, “Calculation of denominator functions for nonstandard finite difference schemes for differential equations satisfying a positivity conditionâ€, SIAM J. Math. Anal. Vol. 33, (2002), 672-691.

[6] R. E. Mickens, Advances in the application of nonstandard finite difference schemes World Scientific Publishing Co. Pte. Ltd. (2005).

[7] R. Chen, Z. Xu and L. Sun, “Finite-difference scheme to solve Schrodinger equationsâ€, Physical Review E, Vol. 47, (1993), 3799-3802.

[8] R. Yaghoubi, H. Saberi Najafi, “Comparison between standard and non-standard finite difference methods for solving first and second order ordinary differential equationsâ€, International Journal of Applied Mathematical Research, Vol. 4, No. 2,(2015), 316-324.

View Full Article: