We show that the theorems of Sanz-Serna and Eirola and Sanz-Serna concerning the symplecticity of Runge-Kutta and Linear Multistep methods respectively, follow from the fact that these methods preserve quadratic integral invariants and are closed under differentiation and restriction to closed subsystems.

The predictor-corrector methods P (EC) with equidistant discretization are applied to the numerical integration of a linear stochastic oscillator. Their ability in preserving the symplecticity, the linear growth property of the second moment, and the oscillation property of the solution of this stochastic system is studied. Their mean-square orders of convergence are discussed. Numerical experi...

Geometric integrators are presented for a class of nonlinear dispersive equations which includes the Camassa-Holm equation, the BBM equation and the hyperelasticrod wave equation. One group of schemes is designed to preserve a global property of the equations: the conservation of energy; while the other one preserves a more local feature of the equations: the multi-symplecticity.

plan irregularity causes local damages being concentrated in the irregular buildings. progressive collapse is also the collapse of a large portion or whole building due to the local damages in the structure. the effect of irregularity on the progressive collapse potential of the buildings is investigated in this study. this is carried out by progressive collapse evaluation of the asymmetric mid...

We present a method to construct symplecticity-preserving renormalization group maps by using the Liouville operator, and obtain correctly reduced symplectic maps describing their long-time behavior even when a resonant island chain appears. PACS-1995: 03.20.+i , 47.20.Ky, 02.30.Mv, 64.60.Ak.