This report presents experimental results for new NAG Fortran Library software for the solution of large sparse symmetric linear systems of algebraic equations Preconditioned conjugate gradient methods introduced at Mark are compared against iterative and direct methods previously available in the library Test problems include discrete approximations to d elliptic partial di erential equations ...

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...

This paper considers two related problems of state estimation and model validation for a class of uncertain linear systems. The main contribution of the paper is that it considers a general information structure which allows for discrete and continuous measurements as well as missing data. The results are given in terms of a recursive state estimator involving a jump Riccati di€erential equatio...

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.

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...

This report presents an experimental comparison of NAG Fortran Library software for the solution of large sparse unsymmetric linear systems of algebraic equations Preconditioned RGMRES CGS and Bi CGSTAB methods to be introduced at Mark are compared against one another and against direct methods Test problems include discrete approximations to D elliptic partial di erential equations random valu...

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...

The transformation which assigns to a linear operator L the recurrence satis ed by coe cient se quences of the polynomial series in its kernel is shown to be an isomorphism of the corresponding operator algebras We use this fact to help factoring q di erence and recurrence operators and to nd nice power series solutions of linear di erential equations In particular we characterize generalized h...

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.

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...