The well-known stochastic Lotka–Volterra model for interacting multi-species in ecology has some typical features: highly nonlinear, positive solution and multi-dimensional. known numerical methods including the tamed/truncated Euler–Maruyama (EM) applied to it do not preserve its positivity. aim of this paper is modify truncated EM establish a new preserving (PPTEM). To simplify proof as well ...

Shallow water equations with a non-flat bottom topography have been widely used to model flows in rivers and coastal areas. An important difficulty arising in these simulations is the appearance of dry areas, as standard numerical methods may fail in the presence of these areas. These equations also have steady state solutions in which the flux gradients are nonzero but exactly balanced by the ...

In this paper, we apply the local discontinuous Galerkin (LDG) method to 2D Keller– Segel (KS) chemotaxis model. We improve the results upon (Y. Epshteyn and A. Kurganov, SIAM Journal on Numerical Analysis, 47 (2008), 368-408) and give optimal rate of convergence under special finite element spaces. Moreover, to construct physically relevant numerical approximations, we develop a positivity-pre...

In this paper we present a shape preserving method of interpolation for scattered data defined in the form of some constraints such as convexity, monotonicity and positivity. We define a k-convex interpolation spline function in a Sobolev space, by minimizing a semi-norm of order k+1, and we discretize it in the space of piecewise polynomial spline functions. The shape preserving condition that...

In this paper, we construct and analyze a uniquely solvable, positivity preserving unconditionally energy stable finite-difference scheme for the periodic three-component Macromolecular Microsphere Composite (MMC) hydrogels system, ternary Cahn-Hilliard system with Flory-Huggins-deGennes free potential. The proposed is based on convex-concave decomposition of given functional two variables, cen...

A positivity-preserving numerical method for nonlinear Black-Scholes models is developed in this paper. The numerical method is based on a nonstandard approximation of the second partial derivative. The scheme is not only unconditionally stable and positive, but also allows us to solve the discrete equation explicitly. Monotone properties are studied in order to avoid unwanted oscillations of t...

This paper is concerned with the model reduction of positive systems. For a given stable positive system, our attention is focused on the construction of a reduced-order model in such a way that the positivity of the original system is preserved and the error system is stable with a prescribed H1 performance. Based upon a system augmentation approach, a novel characterization on the stability w...

This work introduces a single-stage, single-step method for the compressible Euler equations that is provably positivitypreserving and can be applied on both Cartesian and unstructured meshes. This method is the first case of a singlestage, single-step method that is simultaneously high-order, positivity-preserving, and operates on unstructured meshes. Time-stepping is accomplished via the Lax-...