Stable parallel elimination for boundary value ODE’s

Abstract. 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 row- and column- reordered version of the usual almost-block-diagonal coecient matrix. Analytical and numerical evidence is presented to show that the algorithm is stable. 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 algebraic parameters. Key words. Parallel algorithms, two-point boundary value problems, Gaussian elimination, stability AMS(MOS) subject classications. 65L10, 65L20, 65W0