Improved Krylov Precise Time Integration Algorithm for Structural Dynamic Equations

An improved Krylov precise time-step integration algorithm is proposed to solve the second-order differential equations with arbitrary excitation directly and efficiently. This method could tackle the complex excitations and improve the computing efficiency by determining the bound of iterative subspace (m) accurately. The upper bound of m could be obtained by computational efficiency analysis, whereas the error estimation is employed to compute the lower bound of m. Hence, the application of the improved Krylov precise time-step integration algorithm could be extended widely by determining the bound of m. Two numerical examples are also presented to demonstrate the practicability and the applicability of the proposed method.