Network flow watermarking schemes have been used to detect stepping stones, which including watermark embedding scheme and detection scheme. Among them, watermark embedding scheme plays a vital part in a watermarking scheme. Most existing watermark embedding schemes are based on using a randomly select the operation time interval and then generated watermark sequence in carrier flow. However, t...

We construct and analyze fully discrete Galerkin (finite-element) methods of high order of accuracy for the numerical solution of the periodic initial-value problem for the Korteweg-de Vries equation. The methods are based on a standard space discretization using smooth periodic splines on a uniform mesh. For the time stepping, we use two schemes of third (resp. fourth) order of accuracy which ...

This paper introduces a three and a four order explicit time stepping method. These methods have high stage order and favorable monotonicity properties. The proposed methods are based on multistagemultistep (MM) schemes that belong to the broader class of general linear methods, which are generalizations of both Runge-Kutta and linear multistep methods. Methods with high stage order alleviate t...

This study aimed to examine the relationships among various stepping parameters, sex, and age in the elderly. Healthy elderly Japanese individuals 60-85 years old (50 males and 61 females) performed 4 types of stepping motions for 20 s. Stepping motions included bilateral stepping (back/forth and right/left) and unilateral stepping (back/forth and right/left). The number of steps, the average c...

Abstract We analyze backward Euler time stepping schemes for a primal DPG formulation of class parabolic problems. Optimal error estimates are shown in natural norm and the L 2 {L^{2}} field variable. For heat equation solution our equals standard Galerkin scheme and, thus, optimal bound...

High-order adaptive methods for fractional differential equations are proposed. The methods rely on a kernel compression scheme for the approximation and localization of the history term. To avoid complications typical to multistep methods, we focus our study on 1-step methods and approximate the local part of the fractional integral by integral deferred correction to enable high order accuracy...