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...

A Fourier pseudospectral time-domain method is applied to wave propagation problems pertinent to computational aeroacoustics. The original algorithm of the Fourier pseudospectral timedomain method works for periodical problems without the interaction with physical boundaries. In this paper we develop a slip wall boundary condition, combined with buffer zone technique to solve some non-periodica...

This paper details a free surface method using an explicit time stepping scheme for use in z-coordinate ocean models. One key property that makes the method especially suitable for climate simulations is its very stable numerical time stepping scheme, which allows for the use of a long density time step, as commonly employed with coarse-resolution rigid-lid models. Additionally, the effects of ...

We develop efficient fast Fourier transform algorithms for pricing and hedging discretely sampled variance products and volatility derivatives under additive processes (time-inhomogeneous Lévy processes). Our numerical algorithms are non-trivial versions of the Fourier space time stepping method to nonlinear path dependent payoff structures, like those in variance products and volatility deriva...

We analyze a time-stepping finite element method for time-fractional partial differential equation with hidden-memory space-time variable order. Due to the coupling of space-dependent order formulation and hidden memory, fractional cannot be split from space destroys monotonicity in discretization. Because these difficulties, numerical analysis fully-discrete proposed model remained untreated l...

Existing approaches for solving the lattice Boltzmann equations with finite difference methods are explicit and semi-implicit; both have certain stability constraints on the time step size. In this work, a fully implicit second-order finite difference scheme is developed. We focus on a parallel, highly scalable, Newton–Krylov–RAS algorithm for the solution of a large sparse nonlinear system of ...

Implicit-explicit (IMEX) time stepping methods can efficiently solve differential equations with both stiff and nonstiff components. IMEX Runge-Kutta methods and IMEX linear multistep methods have been studied in the literature. In this paper we study new implicit-explicit methods of general linear type (IMEX-GLMs). We develop an order conditions theory for high stage order partitioned GLMs tha...

Developing robust and ecient numerical solution methods for Richards' equation (RE) continues to be a challenge for certain problems. We consider such a problem here: in®ltration into unsaturated porous media initially at static conditions for uniform and non-uniform pore size media. For ponded boundary conditions, a sharp in®ltration front results, which propagates through the media. We evalu...

Abstract. In this paper we develop a two-grid convergence theory for the parallel-in-time scheme known as multigrid reduction in time (MGRIT), as it is implemented in the open-source XBraid package [25]. MGRIT is a scalable and multi-level approach to parallel-in-time simulations that non-intrusively uses existing time-stepping schemes, and that in a specific two-level setting is equivalent to ...

We introduce a novel local time-stepping technique for marching-in-time algorithms. The technique is denoted as Causal-Path Local Time-Stepping (CPLTS) and it is applied for two time integration techniques: fourth order low–storage explicit Runge–Kutta (LSERK4) and second order Leapfrog (LF2). The CPLTS method is applied to evolve Maxwell’s curl equations using a Discontinuous Galerkin (DG) sch...