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Comparative Study of Different Time Integration Algorithms for Solving Kinematic Problems
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DOI：10.3390/modelling7030095.png)
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Abstract
En 中文
This study selects five numerical methods: the explicit Leap-Frog scheme, the implicit Crank-Nicolson scheme, the explicit second-order Runge-Kutta scheme, the implicit Newmark-beta scheme, and the implicit Bathe scheme. These methods are compared through representative dynamic cases in terms of solution accuracy and computational efficiency. The results demonstrate that implicit schemes maintain numerical convergence even with relatively large time steps. The findings also indicate that, although the actual convergence accuracy of the given schemes varies slightly among motion models of different dimensions, it remains close to the theoretical second-order accuracy. Different time integration schemes exhibit distinct numerical accuracies when applied to multi-dimensional motion problems. Overall, under identical time step sizes, the Bathe time integration scheme demonstrates slightly superior computational accuracy and error stability compared to other schemes considered. The numerical efficiency of time integration schemes also varies across dimensions and problem types. The actual computational time does not scale linearly with the time step size and is partially influenced by the complexity of the solution algorithm employed. In general, when solution accuracy is comparable, the Leap-Frog scheme shows marginally higher efficiency in explicit simulations, whereas the Crank-Nicolson scheme proves more efficient in implicit simulations.
Keywords:
time integration scheme
stability analysis
kinematic solution
numerical methods
explicit and implicit schemes