کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4645968 | 1342073 | 2009 | 19 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Exponential Runge–Kutta methods for the Schrödinger equation Exponential Runge–Kutta methods for the Schrödinger equation](/preview/png/4645968.png)
We consider exponential Runge–Kutta methods of collocation type, and use them to solve linear and semi-linear Schrödinger Cauchy problems on the d-dimensional torus. We prove that in both cases (linear and non-linear) and with suitable assumptions, s-stage methods are of order s and we give sufficient conditions to achieve orders s+1 and s+2. We show and explain the effects of resonant time steps that occur when solving linear Schrödinger problems on a finite time interval with such methods. This work is inspired by [M. Hochbruck, A. Ostermann, Exponential Runge–Kutta methods for parabolic problems, Appl. Numer. Math. 53 (2–4) (2005) 323-339], where exponential Runge–Kutta methods of collocation type are applied to parabolic Cauchy problems. We compare our results with those obtained for parabolic problems and provide numerical experiments for illustration.
Journal: Applied Numerical Mathematics - Volume 59, Issue 8, August 2009, Pages 1839-1857