implicit time integration scheme; composite time integration; numerical stability; numerical dissipation; energy conserving/decaying algorithms.

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 divided further into two substeps which may not be necessarily equal. In the first substep, the Newmark scheme is employed an d the three point backward Euler scheme is used in the second substep. The proposed scheme is applied to non-linear problems to study the transient response solution under large deformations and long time durations.