The purpose of these notes is to give some examples illustrating how naive numerical approximations to PDE's may not work at all as expected. In addition, the following two important notions are introduced: (I) von Neumann stability analysis | helps identify when (and if) numerical schemes behave properly. (II) Arti cial viscosity | a tool in stabilizing numerical schemes. These notes should be...

In this paper, we study the qualitative behaviour of approximation schemes for Backward Stochastic Differential Equations (BSDEs) by introducing a new notion of numerical stability. For the Euler scheme, we provide sufficient conditions in the one-dimensional and multidimensional case to guarantee the numerical stability. We then perform a classical Von Neumann stability analysis in the case of...

in this paper some algebraic structures for linguistic fuzzy models are defined for the first time. by definition linguistic fuzzy norm, stability of these systems can be considered. two methods (normed-based & graphical-based) for stability analysis of linguist fuzzy systems will be presented. at the follow a new simple method for linguistic fuzzy numbers calculations is defined. at the end tw...

this paper investigates the stability analysis of fuzzy relational dynamic systems. a new approach is introduced and a set of sufficient conditions is derived which sustains the unique globally asymptotically stable equilibrium point in a first-order fuzzy relational dynamic system with sumproduct fuzzy composition. this approach is also investigated for other types of fuzzy relational composit...

Inspired by the theory of modified equations (backward error analysis), a new approach to high-order, structure-preserving numerical integrators for ordinary differential equations is developed. This approach is illustrated with the implicit midpoint rule applied to the full dynamics of the free rigid body. Special attention is paid to methods represented as B-series, for which explicit formula...

Small-gain statements play a key role in system analysis. These results state that the interconnection of two stable systems is stable provided that the closed loop gain is less than unity. This intuitively satisfying statement can be made rigorous in a number of ways depending on the notion of stability and the family of systems under consideration. Such results were originally given in the 19...

In this article, we develop a set of partial differential equations describing the flow of a dusty fluid in variable porosity media. The developed equations take into account the effect of the porous microstructure on the flowing phases. We presented and overview of the equations governing the flow of a dusty gas in various type media, including that in naturally occurring porous media. Numeric...

to evaluate genotype × environment interaction (gei) of grapevine, 20 genotypes of grapevines with russian origin were evaluated at one location in urmia and four locations in takestan (two locations under full irrigation and two locations under drought stress). this research was performed in a randomized complete block design with three replications and three vines in each plot, in 2012-2013 s...