We present waveform relaxation of linear integral-di erential equations which occur in circuit simulation. We give su cient conditions for convergence and numerical experiments to verify the theoretical results.

We prove an existence and uniqueness theorem for backward stochastic di erential equations driven by a Brownian motion, where the uniform Lipschitz continuity is replaced by a stochastic one.

An exact solution of a system of coupled di erential equations describing the dynamics of a special class of winner-take-all networks is given. From the solution two properties of the short-termmemory traces are derived: (1) information preservation and (2) a discrimination measure. These properties justify a biologically inspired fault tolerant extension of the network using di erentiating neu...

The equivalent, second equivalent and (simply) modi®ed equations for the implicit midpoint rule are shown to be asymptotically equivalent in the sense that an asymptotic analysis of these equations with the time step size as small parameter yields exactly the same results; for linear problems with constant coecients, they are also equivalent to the original ®nite di€erence scheme. Straightforw...

Transfer functions models of linear systems are a well established tool for the design and analysis of one-dimensional systems. This is not the case for multidimensional physical systems, given in terms of initial boundary value problems. Here, the only mathematical description of widespread use are partial di erential equations. This contribution shows, how the one-dimensional transfer functio...

We synthesize robust nonlinear static output feedback controllers for systems of quasi-linear parabolic partial di!erential equations with time-dependent spatial domains and uncertain variables. The controllers are successfully applied to a typical di!usion}reaction process with moving boundary and uncertainty. ( 2000 Elsevier Science Ltd. All rights reserved.

We will discuss here Dirichlet problems for non linear …rst order partial di¤erential equations. We will present the recent results of DacorognaMarcellini on this subject; mentioning brie‡y, as a matter of introduction, some results on viscosity solutions.

one of the ecient and powerful schemes to solve linear and nonlinear equationsis homotopy analysis method (ham). in this work, we obtain the approximate solution ofa system of partial dierential equations (pdes) by means of ham. for this purpose, wedevelop the concept of ham for a system of pdes as a matrix form. then, we prove theconvergence theorem and apply the proposed method to nd the a...

We announce publicly available Fortran software for the initial value problem IVP in ordinary di erential equations ODEs We describe the interfaces and how Fortran language features a ord the opportunity both to address di erent types and structures of variables and to provide functionality not usually directly associated with IVP solvers

Fractional calculus is a natural extension of the integer order calculus and recently, a large number of applied problems have been formulated on fractional di¤erential equations. Analytical solution of many applications, where the fractional di¤erential equations appear, cannot be established. Therefore, cubic polynomial spline function is considered to …nd approximate solution for fractional ...