Abstract
The generalized-α method encompasses a wide range of time integrators. The method possesses high-frequency dissipation while minimizing unwanted low-frequency dissipation. Additionally, the numerical dissipation can be controlled by the user by setting a single parameter, ρ∞. The method is unconditionally stable and has second-order accuracy in time. We extend the second-order generalized-α method to third-order in time while the numerical dissipation can be controlled by a single parameter. In each time step, the scheme only requires inverting one matrix on acceleration and update the displacement and velocity explicitly. We establish that the third-order method is unconditionally stable. We discuss a possible path to the generalization to higher order schemes. All these high-order schemes can be easily implemented into programs that already contain the second-order generalized-α method.
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