Stable parallel elimination for boundary value ODEs (Q1330389)

Linear algebraic systems originating from two-point boundary value problems for systems of ordinary differential equations (ODEs) are solved by parallelizable vectorizable algorithms equivalent to Gaussian elimination with partial row pivoting applied to a version of almost block-diagonal coefficient matrices. As can be expected, in contrast to the use of orthogonal transformation methods, the present approach requires less floating-point operations and shows stability in most circumstances. Numerical results including computational times are reported.