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a-contraction A-stable algebraic function analysis applications approximation assume attractor attracts bounded sets Banach space bounded sets coefficients comparison completely continuous consider consistency convex Crandall and P.L. defined denote derivatives eigenvalues element equilibrium points equivalent error constant estimates example exists finite following result given global error gradient system Grigorieff Hamilton-Jacobi equations Hence holds hyperbolic implies inequality initial value problems integration Jeltsch k-step L-convergence Lemma linear multistep methods linear operator Lipschitz Lipschitz continuous m-stage formula M.G. Crandall maps Math maximum norm modulus Nevanlinna null set obtain orbit original problem P.L. Lions partial differential equations Peano kernel perturbations point dissipative polynomial precompact proof of Theorem properties prove Remark resp root locus Sanz-Serna satisfies second paradigm Section semigroup stability region Theorem 2.1 theory truncation error uniformly bounded unique vector viscosity solutions zeros