Stable parallel elimination for boundary value odes

Summary.A parallelizable and vectorizable algorithm for solving linear algebraic systems arising from two-point boundary value ODEs is described. The method is equivalent to Gaussian elimination, with row partial pivoting, applied to a certain column-reordered version of the usual almost-block-diagonal coefficient matrix. We present analytical and numerical evidence to show that the algorithm is stable in most circumstances. Results from implementation on a shared-memory multiprocessor and a vector processor are given. The approach can be extended to handle problems with multipoint and integral conditions or with algebraic parameters.