In many physical models ordinary differential equations (ODEs) arise with the general form, y'(t)-f(t, y) + g(t), in which abrupt but large changes of limited duration, known as pulses, occur in g(t). These pulses may begin at times which are not known beforehand and may have unknown durations. If the duration is sufficiently short, standard differential equation solvers may miss the pulse comp...

Introduction Partial differential equations on bounded domains of R n have traditionally been equipped with homogeneous boundary conditions (usually Dirichlet, Neumann, or Robin). However, other kinds of boundary conditions can also be considered, and for a number of concrete application it seems that dynamic (i.e., time-dependent) boundary conditions are the right ones. Motivated by physical p...

As scientiic technology becomes increasingly more sophisticated, the production of more data and/or the modelling of more complex systems requires computers with ever-increasing computational power. In order to cope with this situation numerical algorithms have to be developed which allow the distribution of both data and code segments over large numbers of processors with the hope that problem...

We consider certain systems of linear operator equations where the n-th order solution is made unique by an initial value taken from the preceeding solution. Such conditions arise in the enumeration of lattice paths with weighted left turns, if the paths are restricted by a lower linear barrier of integer slope. 1 Introduction All our lattice paths take unit steps in the " North (= y) and ! Eas...

In this paper, fuzzy initial value problems for modelling aspects of uncertainty in dynam­ ical systems are introduced and interpreted from a probabilistic point ofview. Due to the uncertainty incorporated in the model, the behavior of dynamical systems modelIed in this way will generally not be unique. Rather, we obtain a large set of trajectories which are more or less compatible with the des...

where Ji = 0 for x0 < 0. The problem is to find necessary and sufficient conditions on B(x, B) such that the initial-boundary value problem (1), (2), (3) is well-posed. Note that all theorems that a;re formulated below will also apply to the case when (1) is a general hyperbolic equation or a hyperbolic system of equations of arbitrary order provided that all components of the characteristic co...

h.0/ D 0; h.t/ D g t; h.t/ ; t 2 Œ0; 1 (1) in h W Œ0; 1 ! R (Figure 1). A simple sufficient condition that guarantees unique existence of solution h is that g be Lipschitz continuous (along its second argument), which is to say, jg.t;y0/ g.t;y1/j L jy0 y1j; t 2 Œ0; 1; y0;y1 2 R (2) for some constant L independent of y0, y1 and t [16]. We are interested in the computational complexity of the ...