Analyzing Geometric Integrators

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


In the previous chapter, we discussed the growth of error in numerical methods for differential equations. We saw that if the time interval is fixed, the error obeys the power law relationship with stepsize that is predicted by the convergence theory. We also saw that this did not contradict the exponential growth in the error with time (when the stepsize is fixed). The latter issue casts doubt on the reliance on the convergence order as a means for assessing the suitability of an integrator for molecular dynamics.


Molecular Dynamic Hamiltonian System Poisson Bracket Potential Energy Function Symplectic Integrator 
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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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