کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
503212 863749 2010 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
An efficient Chebyshev–Tau spectral method for Ginzburg–Landau–Schrödinger equations
موضوعات مرتبط
مهندسی و علوم پایه شیمی شیمی تئوریک و عملی
پیش نمایش صفحه اول مقاله
An efficient Chebyshev–Tau spectral method for Ginzburg–Landau–Schrödinger equations
چکیده انگلیسی

We propose an efficient time-splitting Chebyshev–Tau spectral method for the Ginzburg–Landau–Schrödinger equation with zero/nonzero far-field boundary conditions. The key technique that we apply is splitting the Ginzburg–Landau–Schrödinger equation in time into two parts, a nonlinear equation and a linear equation. The nonlinear equation is solved exactly; while the linear equation in one dimension is solved with Chebyshev–Tau spectral discretization in space and Crank–Nicolson method in time. The associated discretized system can be solved very efficiently since they can be decoupled into two systems, one for the odd coefficients, the other for the even coefficients. The associated matrices have a quasi-tridiagonal structure which allows a direction solution to be obtained. The computation cost of the method in one dimension is O(Nlog(N))O(Nlog(N)) compared with that of the non-optimized one, which is O(N2)O(N2). By applying the alternating direction implicit (ADI) technique, we extend this efficient method to solve the Ginzburg–Landau–Schrödinger equation both in two dimensions and in three dimensions, respectively. Numerical accuracy tests of the method in one dimension, two dimensions and three dimensions are presented. Application of the method to study the semi-classical limits of Ginzburg–Landau–Schrödinger equation in one dimension and the two-dimensional quantized vortex dynamics in the Ginzburg–Landau–Schrödinger equation are also presented.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computer Physics Communications - Volume 181, Issue 2, February 2010, Pages 325–340
نویسندگان
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