Let (Î±, Î²) âŠ† R denote the maximal interval of existence of solutions for the initial-value problem { dx dt = f(t, x), x(t0) = x0, where E is an open subset of Rm+1, f is continuous in E and (t0, x0)â€¦ (More)

We study Turing computability of the solution operators of the initial-value problems for the linear SchrÃ¶dinger equation ut = i u + and the nonlinear SchrÃ¶dinger equation of the form iut = âˆ’ u + muâ€¦ (More)

Let S be the domain of attraction of a computable and asymptotically stable hyperbolic equilibrium point of the non-linear system áº‹ = f(x). We show that the problem of determining S isâ€¦ (More)

This paper is about a new research field called Web Intelligence (WI for short). We try to explain the needs for coining the term as a sub-discipline of computer science for systematic studies onâ€¦ (More)

The topic of this note is the computability/noncomputability of wave propagation. The authors extend a result obtained by Pour-El/Richards in 1]. We consider the initial value problem for the waveâ€¦ (More)

The theory of generalized functions is the foundation of the modern theory of partial differential equations (PDE). As computers are playing an ever-larger role in solving PDEs, it is important toâ€¦ (More)

In this note we investigate the problem of computing the domain of attraction of a flow on R for a given attractor. We consider an operator that takes two inputs, the description of the flow and aâ€¦ (More)