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A Variational Symplectic Scheme Based on Lobatto's Quadrature
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DOI：10.1007/978-3-032-03921-7_34.png)
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Abstract
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We present a variational integrator based on the Lobatto quadrature for the time integration of dynamical systems issued from the least action principle. This numerical method uses a cubic interpolation of the states and the action is approximated at each time step by Lobattos formula. Numerical analysis is performed on both a harmonic oscillator and a nonlinear pendulum. The geometric scheme is conditionally stable, sixth-order accurate, and symplectic. It preserves an approximate energy quantity. Simulation results illustrate the performance and the superconvergence of the proposed method. [GSI 2025, 26 June 2025.]
Keywords:
ordinary differential equations
harmonic oscillator
nonlinear pendulum
numerical analysis
geometric mechanics
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