LINEAR-SYSTEM SOLVERS FOR BOUNDARY-VALUE ODES

We investigate the stability properties of several linear system solvers for solving boundary value ODEs. We consider the compactification algorithm, Gaussian elimination with row partial pivoting, and a QR algorithm applied to linear systems arising from solving BVPs for which the matrix is block-bidiagonal except for bordering along the last n rows and columns. We will particularly compare AUTO's original linear solver (an LU decomposition with partial pivoting) and our implementation of the analogous QR algorithm to AUTO. Two other factors (the underlying continuation strategy and mesh selection strategy) may affect the stability of the linear system solver for ODE continuation codes as well and are also discussed in our numerical investigations.