LAUSR

Abstract In this study, four sets of novel and enhanced two-stage explicit time integration schemes are developed based on a unified set of unconventional approximations. For the development of explicit schemes, truncated Taylor’s series expansions of the displacement and velocity vectors are used with adjustable algorithmic parameters. Four different sets of algorithmic parameters are proposed to achieve enhanced accuracy and stability of the proposed schemes. Among the four novel schemes, two schemes can adjust a full range of numerical dissipation through one of the algorithmic parameters, and the other two schemes have noticeably increased accuracies. Three of the new schemes have much smaller period errors than those of any existing time-integration schemes. Various linear and nonlinear test problems are solved by using the proposed and existing two-stage schemes, and numerical results are compared to illustrate improved performances of the proposed schemes.