We present an overview of intrinsic integration schemes for di erential equations evolving on manifolds, paying particular attention to homogeneous spaces. Various examples of applications are introduced, showing the generality of the methods. Finally we discuss abstract Runge{Kutta methods. We argue that homogeneous spaces are the natural structures for the study and the analysis of these meth...

In this paper we consider the problem of constructing a well-posed state space model for a class of singular integro-diierential equations of neutral type. The work is motivated by the need to develop a framework for the analysis of numerical methods for designing control laws for aeroelastic and other uid/structure systems. Semigroup theory is used to establish existence and well-posedness res...

For linear di erential algebraic equations of tractability index the notion of the adjoint equation is analysed in full detail Its solvability is shown at the lowest possible smoothness The fundamental matrices of both equations are de ned and their relationships are characterized

The input output decoupling problem for discrete time nonlinear systems by static output feedback is studied in this paper The discrete time nonlinear system is described either by state equations or by high order input output di erence equations NARMA model In both cases the necessary and su cient conditions are given for the solution of the problem Copyright c IFA C

In this paper we describe how wavelets may be used to solve partial diierential equations. These problems are currently solved by techniques such as nite diierences, nite elements and multi-grid. The wavelet method, however, ooers several advantages over traditional methods. Wavelets have the ability to represent functions at diierent levels of resolution, thereby providing a logical means of d...

— We present recent existence results of quasi-periodic solutions for Schrödinger equations with a multiplicative potential on T , db 1, finitely di¤erentiable nonlinearities, and tangential frequencies constrained along a pre-assigned direction. The solutions have only Sobolev regularity both in time and space. If the nonlinearity and the potential are in Cl then the solutions are in Cl. The p...

Interval methods for ordinary di erential equations (ODEs) provide guaranteed enclosures of the solutions and numerical proofs of existence and unicity of the solution. Unfortunately, they may result in large over-approximations of the solution because of the loss of precision in interval computations and the wrapping e ect. The main open issue in this area is to nd tighter enclosures of the so...

In this paper we continue our considerations in on two scale di erence equations mainly with respect to continuous solutions Moreover we study re nable step functions and piecewise polynomials Also solutions with noncompact support are considered New algorithms for the approximative computation of continuous solutions are derived

Up owing salty groundwater, evaporating completely at the ground surface, leads to the buildup of a saline boundary layer, usually with solid salt on the surface. The di usion layer below the surface, if stable, may grow to a nite thickness at equilibrium between the up owing salt and downward di usion. Because of the di erent densities of the uids (low fresh water density in the deeper undergr...

A parallel computational solver for the unsteady incompressible three-dimensional Navier± Stokes equations implemented for the numerical simulation of shear ¯ow cases is presented. The computational algorithms include Fourier expansions in the streamwise and spanwise directions, second-order centered ®nite di€erences in the direction orthogonal to the solid walls, third-order Runge±Kutta proced...