A framework is presented allowing dual-rate numerical integration of the equations of mechanical system dynamics to be considered as a form of Partitioned Runge-Kutta (PRK) integration. Certain coefficients of a PRK integrator are set to zero, so that Runge-Kutta integrators that constitute the PRK integrator can be made to have different numbers of stages. As a result, one Runge-Kutta integrator requires fewer function evaluations than the other does, which is a form of dual-rate integration. Well-established order of accuracy theory for PRK integrators is used to develop a rigorous methodology for designing explicit PRK dual-rate integrators. Stabilized Runge-Kutta theory developed for single-rate RungeKutta integrators is combined with PRK integrator theory to design PRK dual-rate integrators with the largest possible stability regions. Dual-rate PRK integrators created using these approaches are used to simulate the dynamics of vehicle systems that contain subsystems with higher frequency response characteristics than do the basic vehicle subsystems.
A framework is presented allowing dual-rate numerical integration of the equations of mechanical system dynamics to be considered as a form of Partitioned Runge-Kutta (PRK) integration. Certain coefficients of a PRK integrator are set to zero, so that Runge-Kutta integrators that constitute the PRK integrator can be made to have different numbers of stages. As a result, one Runge-Kutta integrator requires fewer function evaluations than the other does, which is a form of dual-rate integration. Well-established order of accuracy theory for PRK integrators is used to develop a rigorous methodology for designing explicit PRK dual-rate integrators. Stabilized Runge-Kutta theory developed for single-rate RungeKutta integrators is combined with PRK integrator theory to design PRK dual-rate integrators with the largest possible stability regions. Dual-rate PRK integrators created using these approaches are used to simulate the dynamics of vehicle systems that contain subsystems with higher frequency response characteristics than do the basic vehicle subsystems.
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