A suite of second-order composite sub-step explicit algorithms with controllable numerical dissipation and maximal stability bounds

Abstract

This paper constructs a composite s-sub-step explicit method and analyzes second-order accuracy, conditional stability, and dissipation control at the bifurcation point. In the present s-sub-step method, each explicit scheme achieves identical second-order accuracy for analyzing general structures and provides maximal stability bound, that is 2×s where s denotes the number of sub-steps. Except for the single-sub-step case, each explicit scheme achieves dissipation control at the bifurcation point. After registering second-order accuracy and controllable numerical dissipation, the composite multi-sub-step explicit method should be well-designed to reach maximal stability bound. The analysis reveals that as the number of sub-steps increases, the developed explicit schemes can reduce numerical low-frequency dissipation and enlarge stability. Under the same computational cost, the advantage of reducing low-frequency dissipation and enlarging stability is gradually weakened with the increase of sub-steps, so the first seven explicit schemes are only developed and compared in this paper. Some typical experiments are provided to confirm the methods’ numerical performance. The proposed explicit schemes are more accurate and efficient for some models than existing second-order algorithms of that class.