It is shown that the fundamental solution of a hyperbolic partial differential equation with time delay has a natural probabilistic structure, i.e. is approximately Gaussian, as t → ∞. The proof uses ideas from the DeMoivre proof of the Central Limit Theorem. It follows that solutions of the hyperbolic equation look approximately like solutions of a diffusion equation with constant convection a...

The steady state of the quasilinear convection-diffusion-reaction equation ut −∇(D(u)∇u) + b(u)∇u+ c(u) = 0 (1) is studied. Depending on the ratio between convection and diffusion coefficients, equation (1) ranges from parabolic to almost hyperbolic. From a numerical point of view two main difficulties can arise related with the existence of layers and/or the non smoothness of the coefficients....

The study of travelling waves or fronts has become an essential part of the mathematical analysis of nonlinear diffusion-convection-reaction processes. Whether or not a nonlinear second-order scalar reaction-convection-diffusion equation admits a travelling-wave solution can be determined by the study of a singular nonlinear integral equation. This article is devoted to demonstrating how this c...

Qinghua Feng School of Science Shandong university of technology Zhangzhou Road 12#, Zibo , Shandong, 255049 China [email protected] Abstract: Based on the concept of decomposition, two alternating group explicit methods are constructed for 1D convection-diffusion equation with variable coefficient and 2D diffusion equations respectively. Both the two methods have the property of unconditional sta...

Convection-diffusion equations are widely used for modeling and simulations of various complex phenomena in science and engineering (Hundsdorfer & Verwer, 2003; Morton, 1996). Since for most application problems it is impossible to solve convection-diffusion equations analytically, efficient numerical algorithms are becoming increasingly important to numerical simulations involving convection-d...

Based on the concept of decomposition, a class of alternating group method is derived for solving convection-diffusion equation with variable coefficient. The method is unconditionally stable, and is suitable for parallel computing.

nanofiltration-based separation processes have found diverse applications in industrial and environmentalproblems recently, due to several advantages such as lower energy requirement and elevated flux ratescompared with their reverse osmosis (ro) counterparts. several attempts have been made for modellingnf-based separation processes ranging from rigorous space-charge approaches to simpler irre...

We introduce a nonlinear DDFV scheme for a convection-diffusion equation. The scheme conserves the mass, satisfies an energy-dissipation inequality and provides positive approximate solutions even on very general grids. Numerical experiments illustrate these properties.

We derive a residual a posteriori error estimates for the subscales stabilization of convection diffusion equation. The estimator yields upper bound on the error which is global and lower bound that is local.

Some least-squares mixed finite element methods for convectiondiffusion problems, steady or nonstationary, are formulated, and convergence of these schemes is analyzed. The main results are that a new optimal a priori L2 error estimate of a least-squares mixed finite element method for a steady convection-diffusion problem is developed and that four fully-discrete leastsquares mixed finite elem...