ON NUMEROV METHOD FOR SOLVING FOURTH ORDER ORDINARY DIFFERENTIAL EQUATIONS
Keywords:Numerov’s method, Runge-Kutta method, Schrodinger equation, Second order, Initial value problems
In this work, a fourth order ODE of the form is transformed into a system of differential equations, that is suitable for solution by means of Numerov method. The obtained solutions are compared with the exact solutions, and are shown to be very effective in solving both initial and boundary value problems in ordinary differential equations.
Adeboye, K. R., Odio, A. O., Salisu, A. & Etuk, S. O. (2018). On the test implementation of the Numerov method. Journal of the Nigerian Association of Mathematical Physics, 45(1): 1-7.
Afolayan, I., Simos, T. E. & Tsitouras, Ch. (2019). Interpolants for sixth-order Numerov-type methods. Mathematical Methods in the Applied Sciences, 42(18): 7349-7358.
Bennett, D. Numerical solution of time-independent 1-D Schrodinger equation. Retrieved from https://www.maths.tcd.ie/~dbennett/js/schro.pdf
Dongjiao, T. (2014). Generalized matrix Numerov solutions to the Schrodinger equation, Bachelor’s thesis, National University of Singapore, Singapore.
Henrici, P. (1962). Discrete Variable Methods in Ordinary Differential Equations: John Wiley. New York.
Killingbeck, J. P. & Jolicard, G. (1999). The eighth order Numerov method. Physics Letters, A261: 40 – 43.
Lambert, J. D. (1973). Computational Methods in Ordinary Differential Equation: Wiley. London.
Mohamed, J. L. (1979). Numerical solution of Y^'' F(X,Y) with particular reference to the radical schrodinger equation, Durham theses, Durham University.
Tsitouras, Ch. & Simos, T. E. (2018). On ninth order explicit Numerov-type methods with constant coefficients. Mediterranean Journal of Mathematics, 15: 46.
Salzman, P. J. (2001). The Numerov algorithm. Retrieved from http://www.sites.google.com /site/phys306307/files/
Simos, T. E. & Tsitouras, Ch. (2020). Explicit ninth order, two step methods for solving inhomogeneous linear problems x^'' (t)=Λx(t)+f(t). Applied Numerical Mathematics, 153: 344-351.
Vigo-Aguiar, J. & Ramos, H. (2005). A variable-step Numerov method for the numerical solution of Schrodinger equation. Journal of Mathematical Chemistry, 37(3): 255-262.
Yasser, A. M. & Nahool, T. A., (2018). A new gate to Numerov’s method. Open Access Journal of Physics, 2(3): 1– 4.
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