It is the object of the present note to present a new nonlinear version of the orthogonal projection method for proving the existence of solutions of nonlinear elliptic boundary value problems. The key point in this method is the application of a new general theorem concerning the solvability of nonlinear functional equations in a reflexive Banach space involving operators which may not be cont...

The parallel solution of Initial Value Problems for Ordinary Diierential Equations has become an active area of research during the past few years. We brieey survey the recent developments in this area, with particular emphasis on traditional forward-step methods that ooer the potential for eeective small-scale parallelism on currently existing machines.

How complex could the solution be to an initial value problem given by a polynomial-time computable function? This question can be given a natural and precise sense in computational complexity theory. In this note, we put together several results stating that more conditions on the problem make the solution simpler. In particular, Lipschitz continuity alone may leave the solution polynomial-spa...