Linear di erential algebraic equations with properly stated leading term are considered via a decoupling into their essential parts. It is shown why for so-called numerically well formulated equations the decoupling and discretizations commute in some sense. In general one cannot expect this commutativity so that additional diÆculties like strong stepsize restrictions may arise. Moreover, abstr...

Since the advent of Taylor Series, polynomial methods have been used to solve di↵erential equations and learn the properties of di↵erential equations. There are many polynomial methods for solving di↵erential equations and understanding dynamical systems. For example, Taylor polynomials, Chebyshev Polynomials and Adomian Polynomials are used to generate approximate solutions. Automatic di↵erent...

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.

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...

We de ne a discrete (integer-valued) Lyapunov function V for cyclic nearest neighbor systems of di erential delay equations possessing a feedback condition. This extends analogous de nitions for cyclic systems of ODE's, and for scalar di erential delay equations. We relate the values of V to the real parts of the Floquet multipliers for such linear periodic systems, and thereby prove all Floque...

in this paper a numerical method for solving forth order fuzzy dierentialequations under generalized differentiability is proposed. this method is basedon the interpolating a solution by piecewise polynomial of degree 8 in the rangeof solution . we investigate the existence and uniqueness of solutions. finally anumerical example is presented to illustrate the accuracy of the new technique.

Some oscillation criteria for the oscillatory behavior of fourth order superlinear dynamic equations on time scales are established. Criteria are proved that ensure that all solutions of superlinear and linear equations are oscillatory. Many of our results are new for corresponding fourth order superlinear di¤erential equations and fourth order superlinear di¤erence equations.

A q-di erence analog of the sixth Painlev e equation is presented. It arises as the condition for preserving the connection matrix of linear q-di erence equations, in close analogy with the monodromy preserving deformation of linear di erential equations. The continuous limit and special solutions in terms of q-hypergeometric functions are also discussed. Mathematical Subject Classi cations (19...

One of the most important theorems in Ordinary Di↵erential Equations is Picard’s Existence and Uniqueness Theorem for first-order ordinary di↵erential equations. Why is Picard’s Theorem so important? One reason is it can be generalized to establish existence and uniqueness results for higher-order ordinary di↵erential equations and for systems of di↵erential equations. Another is that it is a g...