We analyze the equations of radiation hydrodynamics under the approximations of flux-limited diffusion and a thermal radiation field, and derive the minimal set of evolution equations that includes all terms that are of leading order in any regime of non-relativistic radiation hydrodynamics. Our equations are accurate to first order in v/c in the static diffusion regime. We give the equations i...

In this research, an unknown space-dependent force function in the wave equation is studied. This a natural continuation of [1] and chapter 2 [2] [3], where finite difference method (FDM)/boundary element (BEM), with separation variables method, were considered. Additional data are given by one end displacement measurement. Moreover, it exchanging boundary condition, extra data, initial conditi...

Discretizations of Langevin diffusions provide a powerful method for sampling and Bayesian inference. However, such discretizations require evaluation the gradient potential function. In several real-world scenarios, obtaining evaluations might either be computationally expensive, or simply impossible. this work, we propose analyze stochastic zeroth-order algorithms discretizing overdamped unde...

In this paper, using the framework of extrapolation, we present an approach for obtaining higher-order τ-leap methods for the Monte Carlo simulation of stochastic chemical kinetics. Specifically, Richardson extrapolation is applied to the expectations of functionals obtained by a fixed-step τ-leap algorithm. We prove that this procedure gives rise to second-order approximations for the first tw...

The cancellation of the 0th order is described by a low-contrast fused-silica grating. In reported works, the high-contrast grating and complicated structure were applied with reasonable and excellent performance. However, the low-contrast grating is proved that it can also cancel the 0th order with the period more than 2λ in this paper. Grating parameters are optimized by using rigorous couple...

Recently, the nonlinearity continuation method has been used to numerically solve boundary value problems for steady-state Richards equation. The can be considered as a predictor-corrector procedure with simplest form which applied date having trivial, zeroth-order predictor. In this article, effect of more sophisticated predictor technique is examined. Numerical experiments are performed finit...