𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A numerical method for two-dimensional Schrödinger equation using collocation and radial basis functions

✍ Scribed by Mehdi Dehghan; Ali Shokri

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
913 KB
Volume
54
Category
Article
ISSN
0898-1221

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, we propose a numerical scheme to solve the two-dimensional (2D) time-dependent Schrödinger equation using collocation points and approximating the solution using multiquadrics (MQ) and the Thin Plate Splines (TPS) Radial Basis Function (RBF). The scheme works in a similar fashion as finite-difference methods. The results of numerical experiments are presented, and are compared with analytical solutions to confirm the good accuracy of the presented scheme.

📜 SIMILAR VOLUMES

A numerical method for one-dimensional n
A numerical method for one-dimensional nonlinear Sine-Gordon equation using collocation and radial basis functions
✍ M. Dehghan; Ali Shokri 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 313 KB 👁 1 views

## Abstract In this article, we propose a numerical scheme to solve the one‐dimensional undamped Sine‐Gordon equation using collocation points and approximating the solution using Thin Plate Splines (TPS) radial basis function (RBF). The scheme works in a similar fashion as finite difference method

A two-dimensional multilevel adaptive fi
A two-dimensional multilevel adaptive finite element method for the time-independent Schrödinger equation
✍ J. Ackermann; R. Roitzsch 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 767 KB

The subject of this study is a multilevel 2D finite element method (FEM) based on a local error estimator and self-adaptive grid refinement as a universal tool for solving stationary Schriidinger eigenvalue problems. Numerical results for standard problems appearing in vibrational motion and molecul