In this article, block BS methods are considered for the numerical solution of Volterra integro-differential equations (VIDEs). Convergence and stability properties are analyzed. A new Matlab code for the solution of VIDEs, called VIDEBS, is presented. Numerical results using a variable stepsize implementation show the effectiveness of the proposed code. 2014 Elsevier Inc. All rights reserved.

This chapter reviews numerical simulations of quantum field theories based on stochastic quantization and the Langevin equation. The topics discussed include renormalization of finite stepsize algorithms, Fourier acceleration, and the relation of the Langevin equation to hybrid stochastic algorithms and hybrid Monte Carlo. Invited chapter to appear in the special supplement “Stochastic Quantiza...

Abstract The Boris algorithm, a closely related variational integrator and newly proposed filtered are studied when they used to numerically integrate the equations of motion charged particle in mildly non-uniform strong magnetic field, taking step sizes that much larger than period Larmor rotations. For algorithm standard (unfiltered) integrator, satisfactory behaviour is only obtained compone...

By the continuous and discrete nonnegative semimartingale convergence theorems, this paper investigates conditions under which the Euler–Maruyama (EM) approximations of stochastic functional differential equations (SFDEs) can share the almost sure exponential stability of the exact solution. Moreover, for sufficiently small stepsize, the decay rate as measured by the Lyapunov exponent can be re...

An iterative method is proposed for the analysis of the steadystate weight fluctuations in an LMS-type adaptive FIR filter. Without the widely used independence assumption, a power series of the weighterror correlation matrix is derived in terms of the stepsize. Some new effects are observed, e.g., a decrease of the weight fluctuations along the tapped-delay line.