A Survey of Parallel Numerical Methods for Initial Value Problems for Ordinary Differential Equations

The parallel solution of Initial Value Problems for Ordinary Differential Equations has become an active area of research during the past few years. We briefly survey the recent developments in this area, with particular emphasis on traditional forward-step methods that offer the potential for effective small-scale parallelism on currently existing machines. Introduction It is widely believed that the only feasible means of solving many important computationally intensive problems in science and engineering is to use parallel computers effectively. As a result, increasing numbers of researchers have begun investigating numerical methods for a wide variety of advanced machine architectures. In this paper, we briefly survey parallel numerical methods for Initial Value Problems (IVPs) for Ordinary Differential Equations (ODEs): y 0 (x) = f(x; y(x)); for x 2 [x 0 ; x e ], y(x 0 ) = y 0 ; (1) where y : R ! R m and f : R \Theta R m ! R m . See also the earlier reviews of Gear [1..