In this paper we prove the convergence of a nite volume scheme to the solution of a Stefan problem, namely the nonlinear diiusion equation ut ?'(u) = v, together with a homogeneous Neumann boundary condition and an initial condition. This is done by means of a priori estimates in L 1 and use of Kolmogorov's theorem on relative compactness of subsets of L 2 .

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...

Let k be a diierence eld with automorphism. Let b be an element of k, and L be a linear ordinary diierence operator with coeecients in k. A classical problem in the theory of diierence equations is to compute all the solutions in k of the equation L(y) = b. If C denotes a constant eld and if k = C(n) and n = n + 1 or n = qn, there are known algorithms (see 2] for example). Manuel Bronstein pres...

in this paper, we consider a particular class of integral equations of the fourth kind and show that tractability and differentiability index of the given system are 3. tractability and dierentiability index are introduced based on the-smoothing property of a volterra integral operator and index reduction procedure, respectively. using the notion of index, we give sucient conditions for the...

In this paper we will consider two algorithms which allow us to obtain second order linear di erence equations for certain families of polynomials. The corresponding algorithms can be implemented in any computer algebra system in order to obtain explicit expressions of the coe cients of the di erence equations. c © 1998 Elsevier Science B.V. All rights reserved. AMS classi cation: 33C45; 42C05

In this paper, we investigate the almost surely asymptotic stability for the nonlinear stochastic di erential delay equations with Markovian switching. Some su0cient criteria on the controllability and robust stability are also established for linear stochastic di erential delay equations with Markovian switching. ? 2003 Elsevier Ltd. All rights reserved.

The e¢ cient and accurate calculation of sensitivities of the price of …nancial derivatives with respect to perturbations of the parameters in the underlying model, the so called ‘Greeks’, remains a great practical challenge in the derivative industry. This is true regardless of whether methods for partial di¤erential equations or stochastic di¤erential equations (Monte Carlo techniques) are be...

Comparative analysis of two ideologically distinct approaches in the theory of fuzzy di"erential equations is given. Domains of applications, advantages and shortcomings of those approaches are described. New de2nitions of solutions to fuzzy di"erential equations are proposed. c © 2002 Elsevier Science B.V. All rights reserved.

It is known that solutions to second order uniformly elliptic and parabolic equations, either in divergence or nondivergence (general) form, are Hölder continuous and satisfy the interior Harnack inequality. We show that even in the one-dimensional case (x ∈ R1), these properties are not preserved for equations of mixed divergence-nondivergence structure: for elliptic equations Di(a 1 ijDju) + ...

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...