A Unified Family of High‐Order Energy‐Conserving Time Integrators for Nonlinear Dynamical Problems

ABSTRACT This paper develops a family of energy‐conserving time integration methods for nonlinear conservative dynamical problems. Constructed within a unified, self‐starting, and single‐solve integration framework, the proposed methods avoid multi‐stage or sub‐step procedures, leading to improved computational efficiency while maintaining robust accuracy. By using a nonlinear conservative single‐degree‐of‐freedom system as a benchmark, the proposed framework systematically derives the conditions under which higher‐order consistency in conserving the total energy can be achieved. Three implicit integrators, called IA1‐L, IA1‐O, and IA1‐E, are designed to minimize the local truncation error in displacement,…

• NN
  National Natural Science Foundation of China

  Awards: 12502066, 12272105
• CP
  China Postdoctoral Science Foundation

  Award: 2024M764165