Some of the traditional methods for boundary value ODEs, such as standard multiple shooting, finite difference 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. \n In this paper parallel shooting and difference methods are examined, a parallel algorithm for the stable solution of the resulting algebraic system is proposed and evaluated, and a parallel algorithm for stiff boundary value problems is proposed.
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