In this paper we consider smooth di erential 1-forms and smooth nonlinear control-a ne systems with (n 1)-inputs evolving on an ndimensional manifold with boundary. These systems are called hypersurface systems under the additional assumption that the drift vector eld and control vector elds span the tangent space to the manifold. We locally classify all structurally stable di erential 1-forms ...

We consider a system of ordinary di erential equations consisting of a singularly perturbed scalar di erential equation of second order and a scalar di erential equation of rst or second order and study a Neuman-Cauchy or a Neuman-Dirichlet problem. We assume that the degenerate equation has two intersecting solutions such that the standard theory for systems of Tichonov's type cannot be applie...

this paper describes an approximating solution, based on lagrange interpolation and spline functions, to treat functional integral equations of fredholm type and volterra type. this method can be extended to functional dierential and integro-dierential equations. for showing eciency of the method we give some numerical examples.

in this paper, the dierential transform method (dtm) is applied to the fisherequation. this method can be used to obtain the exact solutions of fisherequation. finally, we give some examples to illustrate the suciency of themethod for solving such nonlinear partial dierential equations. these resultsshow that this technique is easy to apply.

In this paper we study polynomial maps of vector spaces zi → Ai1i2···is i zi1zi2zi3 · · · zis and their eigenvectors and eigenvalues. The new quantity called complanart is de ned. Complanarts determine complanarity of solution vectors of systems of polynomial equations. Evaluation of complanart is reduced to evaluation of resultants. As in linear case, the pattern of eigenvectors de nes the pha...

In this paper, a numerical method is presented for proving the existence and inclusion of connecting orbits of continuous dynamical systems described by parameterized nonlinear ordinary di erential equations. Taking a certain second order nonlinear ordinary di erential equaiton as an example, the existence of homoclinic bifurcation points is proved by the method.

Symbolic Reachability Computation for Families of Linear Vector Fields Gerardo Lafferriere Department of Mathematical Sciences Portland State University, P.O. Box 751, Portland, OR 97207-0751. [email protected] George J. Pappas Department of Electrical Engineering University of Pennsylvania, 200 South 33rd Street, Philadelphia, PA 19104. [email protected] Sergio Yovine VERIMAG Centre Equat...

The suitability of methods from multidimensional systems theory and digital signal processing for the e cient simulation of time and space dependent problems has already been demonstrated. Properly chosen functional transformations for the time and space coordinates turn a partial di erential equation into a transfer function description of a multidimensional continuous system. It serves as the...

An approach for transforming systems of partial di erential equations in order to obtain new formulations which are more accessible to numerical solution is studied. An algorithm is developed for generating such transformations automatically, using symbolic computations employing Gr obner bases. The algorithm is implemented using freely available software. This approach, along with planned dev...

in this paper, we present the numerical solution of ordinary dierential equations (or sdes), from each order especially second-order with time-varying and gaussian random coecients. we indicate a complete analysis for second-order equations in special case of scalar linear second-order equations (damped harmonic oscillators with additive or multi- plicative noises). making stochastic dierent...