Implicit time integration scheme; composite time integration; numerical stability.

This paper proposes a simple extension to a collocation based composite time integration proposed by Silva and Bezerra. In this scheme, each time step is further divided into two substeps which may not be necessarily equal. In the first substep, the Newmark scheme is employed and the three point backward Euler scheme is used in the second substep. Stability analysis of the scheme is performed and spectral radius, period elongation, and amplitude decay are discussed. The influence of Newmark parameters and substep sizes on stability and accuracy is studied in detail.