On Enhanced Second-Order Explicit Integration Methods with Controllable Algorithmic Dissipation and Adjustable Sub-Step Size for Hyperbolic Problems

Abstract

This paper constructs and analyzes a generalized composite two-sub-step explicit method to solve various dynamical problems effectively. Via the accuracy and dissipation analysis, the constructed explicit method is further developed into two novel members that achieve identical second-order accuracy, controllable algorithmic dissipation, and desired stability. Unlike all existing explicit schemes, the novel members employ two independent integration parameters ([Formula: see text] and [Formula: see text]) to control numerical features. The parameter [Formula: see text], denoting the splitting ratio of sub-step size, can determine the instant at which external loads are calculated, whereas another parameter [Formula: see text], denoting the spectral radius at the bifurcation point, can control numerical dissipation imposed. Independently adjusting the sub-step size is one significant advantage for solving dynamical problems triggered by discontinuous loads. This paper also provides two novel explicit members’ single-parameter versions for inexperienced users. Besides, the novel explicit members achieve a smaller local truncation error in acceleration, thus enhancing the solution accuracy in displacement and velocity. Numerical examples are solved to validate the significant superiority of the novel members in the solution accuracy.