High-order generalized-$α$ methods
This provides a new time integration scheme for computational mechanics and related fields that require higher-order accuracy with controlled dissipation.
The authors extend the second-order generalized-$\\alpha$ method to third-order accuracy in time while maintaining controllable numerical dissipation and unconditional stability, with a path to higher-order generalization.
The generalized-$α$ method encompasses a wide range of time integrators. The method possesses high-frequency dissipation while minimizing unwanted low-frequency dissipation and the numerical dissipation can be controlled by the user. The method is unconditionally stable and is of 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 in a similar fashion. 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.