Two simple fast integration methods for large-scale dynamic problems in engineering

TLDR: A new simple explicit two-step method and a new family of predictor–corrector integration algorithms are developed for use in the solution of numerical responses of dynamic problems, avoiding solving simultaneous linear algebraic equations in each time step.

Abstract: A new simple explicit two-step method and a new family of predictor–corrector integration algorithms are developed for use in the solution of numerical responses of dynamic problems. The proposed integration methods avoid solving simultaneous linear algebraic equations in each time step, which is valid for arbitrary damping matrix and diagonal mass matrix frequently encountered in practical engineering dynamic systems. Accordingly, computational speeds of the new methods applied to large system analysis can be far higher than those of other popular methods. Accuracy, stability and numerical dissipation are investigated. Linear and nonlinear examples for verification and applications of the new methods to large-scale dynamic problems in railway engineering are given. The proposed methods can be used as fast and economical calculation tools for solving large-scale nonlinear dynamic problems in engineering.