Abstract
Recent developments in the theory of stability or contractivity of numerical methods for solving ordinary differential equations (see for instance [4], [5], [8]) have renewed the interest for the study of quadrature formulas with positive weights. Norsett-Wanner [8] and Burrage [2], [3] have given characterisation of such quadrature formulas of order ≧2m−2 or ≧2m−3. In this paper we extend these investigations to the case of formulas of order ≧2m−4 and then to the case where the order is ≧2m−7. Finally we use these results to characterise the algebraically stable methods out of a 12-parameter family of implicit Runge-Kutta methods of order 2m−4.
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