𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Fredholm integral equation method for the integro-differential Schrödinger equation

✍ Scribed by Ick-Soon Chang; Sheon-Young Kang


Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
287 KB
Volume
56
Category
Article
ISSN
0898-1221

No coin nor oath required. For personal study only.

✦ Synopsis


A new method based on the Clenshaw-Curtis quadrature for the numerical solution of the integro-differential Schrödinger equation is investigated. The method shows that it converges quickly and the truncation errors decrease faster than any power of the inverse number of the Chebyshev support points. Discretization technique is presented in detail. Accompanying C ++ code for the Fredholm type method is available upon request.


📜 SIMILAR VOLUMES


Integral Equation Method for Coupled Sch
✍ R.A. Gonzales; S.-Y. Kang; I. Koltracht; G. Rawitscher 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 246 KB

A new integral equation method for the numerical solution of the radial Schrödinger equation in one dimension, developed by the authors (1997, J. Comput. Phys. 134, 134), is extended to systems of coupled Schrödinger equations with both positive and negative channel energies. The method, carried out

Geometric Integrators for the Nonlinear
✍ A.L. Islas; D.A. Karpeev; C.M. Schober 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 270 KB

Recently an interesting new class of PDE integrators, multisymplectic schemes, has been introduced for solving systems possessing a certain multisymplectic structure. Some of the characteristic features of the method are its local nature (independent of boundary conditions) and an equal treatment of

Symplectic methods for the nonlinear Sch
✍ Y.-F. Tang; L. Vázquez; F. Zhang; V.M. Pérez-García 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 528 KB

In this paper, we show that the spatial discretization of the nonlinear SchrSdinger equation leads to a Hamiltonian system, which can be simulated with symplectic numerical schemes. In particular, we apply two symplectic integrators to the nonlinear SchrSdinger equation, and we demonstrate that the

Exponential fitted methods for the numer
✍ T.E. Simos 📂 Article 📅 1992 🏛 Elsevier Science 🌐 English ⚖ 500 KB

A new sixth-order Runge-Kutta type method is developed for the numerical integration of the one-dimensional Schrodinger equation. The formula developed contains certain free parameters which allows it to be fitted automatically to exponential functions. We give a comparative error analysis with othe