BIT Numerical Mathematics

, Volume 58, Issue 2, pp 457–488 | Cite as

Lagrangian and Hamiltonian Taylor variational integrators

  • Jeremy Schmitt
  • Tatiana Shingel
  • Melvin Leok


In this paper, we present a variational integrator that is based on an approximation of the Euler–Lagrange boundary-value problem via Taylor’s method. This can be viewed as a special case of the shooting-based variational integrator. The Taylor variational integrator exploits the structure of the Taylor method, which results in a shooting method that is one order higher compared to other shooting methods based on a one-step method of the same order. In addition, this method can generate quadrature nodal evaluations at the cost of a polynomial evaluation, which may increase its efficiency relative to other shooting-based variational integrators. A symmetric version of the method is proposed, and numerical experiments are conducted to exhibit the efficacy and efficiency of the method.


Geometric numerical integration Variational integrators Symplectic integrators Hamiltonian mechanics 

Mathematics Subject Classification

37M15 65P10 70H05 


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© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaSan DiegoUSA

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