The “t-model” for dimensional reduction is applied to the estimation of the rate of decay of solutions of the Burgers equation and of the Euler equations in two and three space dimensions. The model was first derived in a statistical mechanics context, but here we analyze it purely as a numerical tool and prove its convergence. In the Burgers case the model captures the rate of decay exactly, a...

In the present paper, we prove that the Wasserstein distance on the space of continuous sample-paths equipped with the supremum norm between the laws of a uniformly elliptic one-dimensional diffusion process and its Euler discretization with N steps is smaller than O(N) where ε is an arbitrary positive constant. This rate is intermediate between the strong error estimation in O(N) obtained when...

1 This report is available by anonymous ftp from ftp.esat.kuleuven.ac.be in the directory pub/SISTA/moreau/reports/. The missing gures, which have been excluded because they are diicult to print, are available separately in the le chua gures.ps. Abstract Composition methods are methods for the integration of ordinary differential equations arising from diierential geometry, or more precisely, L...

Abstract: New numerical techniques are presented for the solution of a class of the variable order fractional advection-diffusion equation with a nonlinear source term on one-dimensional finite domain. Quasiwavelet and double quasi-wavelet are used for the spatial discretization. For the time stepping, Euler method is considered. We also tested the method proposed on several problems with very ...

This paper deals with the numerical analysis of an upscaled model describing the reactive flow in a porous medium. The solutes are transported by advection and diffusion and undergo precipitation and dissolution. The reaction term and, in particular, the dissolution term have a particular, multivalued character, which leads to stiff dissolution fronts. We consider the Euler implicit method for ...

We describe a new family of weak p-th order accurate SDE time integration schemes, called the Direct Richardson p-th order accurate (DRp) schemes. The DRp schemes use the idea of Richardson extrapolation on Euler time steps, performed by way of an acceptance-rejection algorithm. Previous applications of Richardson extrapolation to the Euler scheme are applicable only when the objective is to es...

In the previous note it was shown how L-Systems can be used to numerically solve systems of partial differential equations, for a constant or growing medium, and the method was applied to computer graphics purposes. The LSystem from the previous section employed a forward Euler method for finite differencing. Although simple to implement, the forward Euler method is in many case inadequate, for...

The spatial discretization of the magnetic vector potential formulation of magnetoquasistatic field problems results in an infinitely stiff differential-algebraic equation system. It is transformed into a finitely stiff ordinary differential equation system by applying a generalized Schur complement. Applying the explicit Euler time integration scheme to this system results in a small maximum s...

In this paper, we consider reinitializing level functions through equation /tþ sgnð/Þðkr/k 1Þ 1⁄4 0 [16]. The method of Russo and Smereka [11] is taken in the spatial discretization of the equation. The spatial discretization is, simply speaking, the second order ENO finite difference with subcell resolution near the interface. Our main interest is on the temporal discretization of the equation...

The exponential stability of continuous-time Hopfield neural networks is not preserved when implemented on digital computers by means of explicit numerical methods, whereas the implicit (or backward) Euler method preserves this exponential stability under exactly the same sufficient conditions as those previously obtained for the continuous model. The proof is based on the nonlinear measure app...