DICHOTOMIC STABILITY AND MULTIPLE SHOOTING FOR NUMERICAL BOUNDARY-VALUE-PROBLEMS IN INDEX-ONE DIFFERENTIAL-ALGEBRAIC EQUATIONS

When solving boundary-value problems (BVPs) in ordinary differential e quations (ODEs), the concept of dichotomic stability can be of importa nce when sharp boundary layers are present. The same concept is clearl y also important for BVPs in differential-algebraic equations (DAEs). A multiple-shooting code uses an initial-value integrator, and a dicho tomically stable integrator has been used for ODEs. Existing multiple- shooting codes for DAEs typically use backward differentiation formula e, and these are not dichotomically stable. We report here on the adap tation of a dichotomically stable integrator for use with DAEs.