THE ANALYSIS OF GENERALIZED BACKWARDS DIFFERENCE FORMULA METHODS APPLIED TO HESSENBERG FORM DIFFERENTIAL-ALGEBRAIC EQUATIONS

The numerical solution of Hessenberg form differential-algebraic equations by variable stepsize, generalized backward difference formulae (GBDF) is studied. GBDF methods of sufficiently high order are shown to converge for problems of index 3 and 4. The proof techniques developed are not sufficiently powerful to show convergence for index 5 problems, although it is speculated that convergence also occurs for these problems.