ON PARALLEL METHODS FOR BOUNDARY-VALUE ODES

Some of the traditional methods for boundary value ODEs, such as standard multiple shooting, finite differences and collocation methods, lend themselves well to parallelization in the independent variable: the first stage of the construction of a solution approximation is performed independently on each subinterval of a mesh. However, the underlying possibly fast bidirectional propagation of information by fundamental modes brings about stability difficulties when information from the different subintervals is combined to form a global solution. Additional difficulties occur when a very stiff problem is to be efficiently and stably solved on a parallel architecture. In this paper difference and parallel shooting methods are examined. A parallel algorithm for the stable solution of the resulting algebraic system is proposed and evaluated. A parallel algorithm for stiff boundary value problems is proposed as well.