Boundary conditions Boundary value problems Functions Hamiltonians Numerical analysis Runge Kutta methods Set theory Adjoint pairs of differential-algebraic equations Differentialalgebraic equations Self-adjoint boundary value problems Self-adjoint equations Differential equations
Issue Date:
2005
Publisher:
Applied Numerical Mathematics
Citation:
Volume 53, Issue 4-Feb, Page 131-148
Abstract:
We consider linear homogeneous differential-algebraic equations A(Dx)?+Bx=0 and their adjoints
-D*(A*x)?+B*x=0 with well-matched leading coefficients in parallel. Assuming that the equations are
tractable with index less than or equal to 2, we give a criterion ensuring the inherent ordinary differential
equations of the pair to be adjoint each to other. We describe the basis pairs in the invariant subspaces that
yield adjoint pairs of essentially underlying ordinary differential equations. For a class of formally selfadjoint
equations, we characterize the boundary conditions that lead to self-adjoint boundary value problems
for the essentially underlying Hamiltonian systems. ?? 2004 IMACS. Published by Elsevier B.V. All rights
reserved.
