A number of key scientific computing applications that are based upon tensor-product grid constructions, such as numerical weather prediction (NWP) and combustion simulations, require property-preserving interpolation. Essentially non-oscillatory (ENO) interpolation is a classic example schemes. In the aforementioned application areas, property preservation often manifests itself requirement fo...

In this paper, we design and analyze third order positivity-preserving discontinuous Galerkin (DG) schemes for solving the time-dependent system of Poisson--Nernst--Planck (PNP) equations, which has found much use in diverse applications. Our DG method with Euler forward time discretization is shown to preserve positivity cell averages at all steps. The numerical solutions then restored by a sc...

In this paper, we propose a class of explicit positivity preserving numerical methods for general stochastic differential equations which have positive solutions. Namely, all the solutions are positive. Under some reasonable conditions, obtain convergence and rate results these methods. The main difficulty is to strong whose coefficients exponential growth. Some experiments provided illustrate ...

A nonlinear noncooperative elliptic system is shown to have a positivity preserving property. That is, there exists a uniform positive constant such that, whenever the noncooperative part is bounded by this constant, positivity of the source term implies that the solution is positive. The model operator is the p-laplacian with 1 < p < ∞ on a one-dimensional domain. The source term appears in on...

Semigroups of positivity preserving linear operators on measures of a measurable space X describe the evolutions of probability distributions of Markov processes on X. Their dual semigroups of positivity preserving linear operators on the space of measurable bounded functions B(X) on X describe the evolutions of averages over the trajectories of these Markov processes. In this paper we introduc...

In Computer Aided Geometric Design it is often needed to produce a positivity preserving curve according to the given positive data. The main focus of this work is to visualize the positive data in such a way that its display looks smooth and pleasant. A rational quadratic trigonometric spline function with three shape parameters has been developed. In the description of the rational quadratic ...

For positive diffusions, we construct split-step second-order weak approximations preserving the positivity property. For illustration, we apply the construction to some popular stochastic differential equations such as Verhulst, CIR, and CKLS equations.

Finite-volume central-upwind schemes for shallow water equations were proposed in [A. Kurganov and G. Petrova, Commun. Math. Sci., 5 (2007), 133–160]. These schemes are capable of maintaining “lake-at-rest” steady states and preserving the positivity of the computed water depth. The well-balanced and positivity preserving features of the central-upwind schemes are achieved, in particular, by us...

We show that, under mild conditions, two well-known definitions for the local property of a Dirichlet form are equivalent. We also show that forms that come from differential operators are local. 1991 AMS Subject Classification: 31C25 The purpose of this paper is to clarify the relationship between two different notions of locality that have appeared in the literature of Dirichlet forms. The fi...