In the stochastic formulation of chemical reactions, the time evolution of the first M order statistical moments for the number of molecules of the different species involved is generally not closed, in the sense that they depend on moments of order higher than M. For analysis purposes, the time evolution of the first M order moments is often made to be closed by approximating the higher order ...

This study was suggested by previous work on the simulation of evolution equations with scale-dependent processes, e.g., wave-propagation or heat-transfer, that are modeled by wave equations or heat equations. Here, we study both parabolic and hyperbolic equations. We focus on ADI (alternating direction implicit) methods and LOD (locally one-dimensional) methods, which are standard splitting me...

In this work, we discuss a collocation method for solving some Rosenau type non-linear higher order evolution equations with Dirichlet’s boundary conditions. The approach used, is based on collocation of a quintic B-splines over finite elements so that we have continuity of the dependent variable and its first four derivatives throughout the solution range. We apply quintic. B-splines for spati...