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Numerical Methods

  • Stavros C. Farantos
Chapter
Part of the SpringerBriefs in Molecular Science book series (BRIEFSMOLECULAR)

Abstract

The theories developed in the previous chapters, classical and quantum mechanical, are put in action by discretizing the corresponding differential equations. The variable order finite difference approximation to the unknown solutions and their derivatives is the preferred method, not only because of their well understood convergence properties and the relatively easy way of their programming, but also, finite differences provide a uniform approach to different type of equations, especially when we work in a Cartesian coordinate system. With respect to Schrödinger equation several grids are examined and comparisons with the more popular pseudospectral methods is made. For the location of periodic orbits the multiple shooting method is developed as it has been thoroughly tested. Finally, computer codes for studying classical nonlinear molecular dynamics and solving the Schrödinger equation are described.

Keywords

Periodic Orbit Pseudospectral Method Finite Difference Approximation Sinc Function Cardinal Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Department of ChemistryUniversity of CreteIraklionGreece
  2. 2.Institute of Electronic Structure and LaserFoundation for Research and Technology-HellasIraklionGreece

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