Martin Arnold
Applying BDF to quasilinear differential-algebraic equations of index 2: a perturbation analysis
Preprint series: Preprints aus dem Fachbereich Mathematik, Universitt Rostock
65L05 Initial value problems
Abstract: For a class of quasilinear differential-algebraic equations (DAEs) of
index 2 the error propagation in analytical and numerical solution of
an initial value problem is studied. Previously obtained error bounds
for backward Euler method applied to DAEs of index 2 in Hessenberg
form are extended to BDF discretizations of quasilinear DAEs. The large
error terms are shown to be concentrated in the algebraic (or
``nullspace'') components of the solution while the differential
components are much more robust against perturbations. For
linear DAEs with time varying coefficients the error bounds can be
further decreased. The results of the theoretical analysis are
illustrated by numerical tests.
Keywords: Differential algebraic equations, perturbation index Backward differentiation