Improvement of discrete-mechanics-type time integration schemes by utilizing balance relations in integral form together with Picard-type iterations. (English) Zbl 1535.70054
Summary: The search for efficient explicit time integration schemes is a relevant topic in the current literature on dynamic mechanical systems. In this paper, we describe a strategy of utilizing the balance relations of mechanics in their integral form, so-called general laws of balance, where the time-evolution of the integrands is approximated by established computational techniques of the discrete-mechanics-type. In a Picard-type iteration, the outcomes are used for repeating the procedure several times, leading to an increased accuracy. The advantages of the present explicit approach are discussed in the context of linear and nonlinear motions of the mathematical pendulum. We utilize the modern symbolic procedures to obtain the time integration formulae and compare the results of our methods with exact solutions and with the results of higher-order implicit methods and also with a recent explicit formulation from the literature.
MSC:
| 70H06 | Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics |
| 65D30 | Numerical integration |
Keywords:
discrete mechanics; Picard iteration; explicit time integration scheme; balance relations; symbolic computation; computer algebraReferences:
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