Using nonstandard finite difference methods for solving converted Schrodinger equation to an ODE

Iranian Journal of Optimization

مقاله 2، دوره 13، شماره 1، خرداد 2021، صفحه 13-27   

نوع مقاله: Research Paper

نویسنده

Farnoosh Izadi^*

Department of Applied Mathematics, Islamic Azad University, Somesara Branch, Somesara, Iran

چکیده

In this work, by introducing a transformation, the nonlinear Schrodinger equation is converted to an ordinary differential equation (ODE). Then, two nonstandard finite difference (NSFD) schemes are constructed for studying the reduced equation. It is shown that the methods preserve the positivity and boundedness properties of the original equation and are stable conditionally and consistence. Finally, the results of the methods are compared with each other and also with the results of the standard finite difference scheme at some points. The graphs of the errors of numerical solutions for these schemes are plotted and compared with the exact solutions.

کلیدواژه‌ها

Schrodinger equation؛ finite difference؛ nonstandard scheme؛ stability؛ consistence

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