We present an AXIOM environment called JET for geometric computations with partial dierential equations within the framework of the jet bundle formalism. This comprises especially the completion of a given dierential equation to an involutive one according to the Cartan-Kuranishi Theorem and the setting up of the determining system for the generators of classical and non-classical Lie symmetrie...

in this paper, we prove the existence of the solution for boundary value prob-lem(bvp) of fractional dierential equations of order q 2 (2; 3]. the kras-noselskii's xed point theorem is applied to establish the results. in addition,we give an detailed example to demonstrate the main result.

The problem of nding adapted solutions to systems of coupled linear forward-backward stochastic dierential equations (FBSDEs, for short) is investigated. A necessary condition of solvability leads to a reduction of general linear FBSDEs to a special one. By some ideas from controllability in control theory, using some functional analysis, we obtain a necessary and sucient condition for the solv...

This paper studies the application of interval analysis and consistency techniques to ordinary di erential equations. It presents a unifying framework to extend traditional numerical techniques to intervals. In particular, it shows how to extend explicit methods to intervals. The paper also took a fresh look at the traditional problems encountered by interval techniques and studied how consiste...

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...

S hur omplement pre onditioning for ellipti systems of partial di erential equations D. Loghin and A. J. Wathen One su essful approa h in the design of solution methods for saddle-point problems requires the eÆ ient solution of the asso iated S hur omplement problem ([26℄, [19℄). In the ase of problems arising from partial di erential equations the fa torization of the symbol of the operator an...

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.

This paper summarizes recent results on the number and characterization of di erential invariants of transformation groups Generalizations of theorems due to Ovsiannikov and to M Green are presented as well as a new approach to nding bounds on the number of independent di erential invariants Consider a group of transformations acting on a jet space coordinatized by the inde pendent variables th...

An initial value problem for y0 = f(t; y) may have an associated event function g(t; y). An event is said to occur at t when g(t ; y(t )) = 0. We consider problems for which the de nition of f(t; y) changes at the time of an event. A number of solvers locate events and restart the integration there so as to deal with the changes in f , but there is little theoretical support for what is done. H...

A transformation is introduced to e!ectively remove level e!ects, i.e. the state dependency of the di!usion function, in a restricted class of multivariate stochastic di!erential equations such that the general continuous}discrete-time nonlinear "ltering problem may be solved using new or existing implementations of the extended kalman "lter (EKF). An implementation of a quasi-maximum likelihoo...