Implicit s-sub-step time integration schemes with (s+1)th-order accuracy and dissipation control

We propose a family of higher-order implicit s-sub-step time integration methods achieving (s+1)th-order accuracy and dissipation control for 2≤s≤5 for the systems under external loadings. These schemes allow users to control numerical dissipation through a parameter ${\rho }_{\infty }$. The methods do not require acceleration vectors during calculations; accelerations can be obtained using a simple process based on higher-order finite differences of the displacements, if needed. To maintain the order of accuracy in systems with external forces, we model the external force at the last sub-step. We present results from several linear and nonlinear examples to validate our theoretical findings, indicating that the proposed method offers more accurate responses compared to conventional methods with similar or reduced computational costs. The MATLAB source code implementing the proposed methods is available at: https://github.com/LeeChanJuKor/HDSUCI.git.