We will present our recent result on the construction of high order WENO finite volume methods for the approximation of hyperbolic partial differential equations on Cartesian grids. The simplest way to use WENO methods on multidimensional Cartesian grids consists in applying a one-dimensional WENO scheme in each direction. This spatial discretization is typically combined with a Runge-Kutta met...

In this paper, a new method is proposed in order to evaluate the stochastic solution of linear random differential equation. The method is based on the combination of the probabilistic transformation method for a single random variable and the numerical methods (e.g. finite difference, finite element, Runge-Kutta, etc...). The transformation technique evaluates the probability density function ...

In this paper we develop a technique for avoiding the order reduction caused by nonconstant boundary conditions in the methods called splitting, alternating direction or, more generally, fractional step methods. Such methods can be viewed as the combination of a semidiscrete in time procedure with a special type of additive Runge–Kutta method, which is called the fractional step Runge–Kutta met...