Continuous system dynamics can be described by possibly large systems of di erential equations These can be either ordinary di erential equations ODEs or contain algebraic constraints as well to form di erential and algebraic equations DAEs Complex systems such as aircraft often operate in di erent modes of continuous operation and when mode changes occur the continuous dynamics change abruptly...

The nite di erence method is a numerical analysis technique used to solve problems involving irregular geometries, complicated boundary conditions, or both. The geometries are represented using partial di erential equations. The solutions to the partial di erential equations can be easily generated with the aid of a computer. As the geometries become increasingly complex, the solutions of the p...

This article presents a numerical method for solving nonlinear two-dimensional fractional Volterra integral equation. We derive the Hat basis functions operational matrix of order integration and use it to solve integro-di?erential equations. The is described illustrated with examples. Also, we give error analysis.

it is known that a stochastic dierential equation (sde) induces two probabilisticobjects, namely a diusion process and a stochastic ow. while the diusion process isdetermined by the innitesimal mean and variance given by the coecients of the sde,this is not the case for the stochastic ow induced by the sde. in order to characterize thestochastic ow uniquely the innitesimal covariance give...

It is proven that an initial value problem of an autonomous system verifying some conditions has exactly one open continuously di€erentiable trajectory on R, whose limit set is not one point. The proof of the result is based upon continuation methods. 1. Preliminaries Di€erential equations play a key role in nature and technology because they control their processes. In time-dependent processes...

The Multiquadric Radial Basis Function (MQ) Method is a meshless collocation method with global basis functions. It is known to have exponentional convergence for interpolation problems. We descretize nonlinear elliptic PDEs by the MQ method. This results in modest size systems of nonlinear algebraic equations which can be eeciently continued by standard continuation software such as auto and c...

We de ne continual queries as a useful tool for monitoring of updated information. Continual queries are standing queries that monitor the source data and notify the users whenever new data matches the query. In addition to periodic refresh, continual queries include Epsilon Transaction concepts to allow users to specify query refresh based on the magnitude of updates. To support e cient proces...

Reference 1] Pavel Krsek, Tomm a s Pajdla, and VV aclav Hlavv a c. Estimation of differential structures on triangulated surfaces. Abstract: This paper presents a method for extracting diierential structures on 3D surfaces and describes an algorithm for estimation of principal curvatures and principal directions from 3D scanned data. The method serves as a base for the extracting intrinsic curv...

The exact solutions of PDEs with ne-scale co-eecients and data contain details that make computations expensive. When only the coarse-scale approximations of the solutions are needed simpler equations can be derived in a process called homogenization. Classical homogenization techniques are based on the analytic expansion of the exact solution. There are also limitations, such as periodic-ity o...

Detecting and extracting modi cations from information sources is an integral part of data warehousing. For unsophisticated sources, in practice it is often necessary to infer modi cations by periodically comparing snapshots of data from the source. Although this snapshot di erential problem is closely related to traditional joins and outerjoins, there are signi cant di erences, which lead to s...