Numerical Integrators

  • Ben Leimkuhler
  • Charles Matthews
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 39)


At its most basic level, molecular dynamics is about mapping out complicated point sets using trajectories of a system of ordinary differential equations (or, in Chaps.  6–8, a stochastic-differential equation system). The sets are typically defined as the collection of probable states for a certain system. In the case of Hamiltonian dynamics, they are directly associated to a region of the energy landscape. The trajectories are the means by which we efficiently explore the energy surface. In this chapter we address the design of numerical methods to calculate trajectories.


Hamiltonian System Global Error Adjoint Method Energy Error Wedge Product 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Ben Leimkuhler
    • 1
  • Charles Matthews
    • 2
  1. 1.School of MathematicsUniversity of EdinburghEdinburghUK
  2. 2.Gordon Center for Integrative ScienceUniversity of ChicagoChicagoUSA

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