Langevin simulation provides an effective way to study collisional effects in beams by reducing the six-dimensional Fokker-Planck equation to a group of stochastic ordinary differential equations. These resulting equations usually have multiplicative noise since the diffusion coefficients in these equations are functions of position and time. Conventional algorithms, e.g. Euler and Heun, give o...

In this paper, we investigate the stability of a numerical method for solving wave equation. The uses explicit leap-frog in time and high order continuous discontinuous (DG) finite elements using standard Lagrange Hermite basis functions space. Matrix eigenvalue analysis is used to calculate time-step restrictions. We show that restriction independent nodal distribution, such as equidistributed...

stability in the autonomous, scalar case was proven in 1963 in Johansson and Kreiss (9), see also (4), and for non-commuting, autonomous systems in 2012 (12), see also (17) for background. We prove herein weak instability in the nonautonomous case. The extension of stability for ODEs from autonomous to nonautonomous (with test problem y′ = λ (t)y) has a rich history. Dahlquist (3) proved that a...

In this work, we discuss the formulation, stability, convergence and numerical validation of a high-order leap-frog based non-dissipative discontinuous Galerkin time-domain (DGTD) method for solving Maxwell’s equations on non-conforming simplicial meshes. This DGTD method makes use of a nodal polynomial interpolation method for the approximation of the electromagnetic field within a simplex, an...

We develop a general strategy in order to implement approximate discrete transparent boundary conditions for finite difference approximations of the two-dimensional transport equation. The computational domain is rectangle equipped with Cartesian grid. For leap-frog scheme, we explain why our provides explicit numerical on four sides and it does not require prescribing any condition at corners ...

The exponential decay law is well established since its first derivation in 1928; however, it not exact but only an approximate description. In recent years some experimental and theoretical indications for non-exponential have been documented. First we solve analytically the time-dependent Schrödinger equation one dimension a potential consisting of infinite wall plus rectangular barrier with ...

Abstract A common migratory pattern in birds is that northerly breeding populations migrate to more southerly non-breeding sites compared ( leap-frog migration ). Not only do experience differences distances, but also different environmental conditions, which may vary spatiotemporally within their annual cycles, creating distinctive selective pressures and strategies. Information about such ada...

We propose and analyze a linear stabilization of the Crank-Nicolson Leap-Frog (CNLF) method that removes all timestep / CFL conditions for stability and controls the unstable mode. It also increases the SPD part of the linear system to be solved at each time step. We give a proof of unconditional stability of the method as well as a proof of unconditional, asymptotic stability of both the stabl...

Most of the existing works view the shapefrom-shading problem as equivalent to a non-linear first-order partial differential equation in surface elevation. Recently, there is a new approach to this problem, namely the shape-from-shading using the heat equation. This paper reviews several works either using the first or the second approach. The previous approach is also implemented in solving th...

In this paper we evaluate the possibilities of one-sided communication, a new feature of the MPI-2 standard, on the Origin2000 for relatively short-range molecular dynamics (MD) simulations. Our algorithm is based on an asynchrony message-passing multi-cell approach using MPI as message-passing layer and the Leap-Frog/ Verlet algorithm for the time integration. We compare an one-sided with two ...