Differential-algebraic Equations and Their Numerical Treatment

analogously arbitrary assumptions of Theorem asymptotically asymptotically stable bijectively boundary value problems BVP's Bx(t canonical normal form compute continuously differentiable convergence Corollary defined Definition denote derive difference schemes differential-algebraic equations equivalent explicit differential equations formulate global index Griepentrog/März Hence hmax holds im(A im(AK implicit implies ind(A ind(A,B ind(A(t inequality initial condition initial value investigate IRK(DAE IVP's Jacobian ker(A ker(A(t ker(D ker(S L(RM Lemma linear DAE's linear multistep methods Lipschitz-continuous matrix function matrix pencil N(to non-singular non-singular matrix non-transferable DAE's nonlinear null-space numerical obtain ODE's one-leg methods one-step method order of consistency P₁ Petzold projector function Proof properties proved regular resp respectively Runge-Kutta methods satisfies singular solution solve stability subspace sufficiently small t₁ tion to,T tractable with index transferable DAE's transformation trivial uniquely solvable valid value problems vector well-posed yields