S. Tracogna

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A general class of variable stepsize continuous two-step Runge-Kutta methods is investigated. These methods depend on stage values at two consecutive steps. The general convergence and order criteria are derived and examples of methods of orderp and stage orderq=p orq=p−1 are given forp≤5. Numerical examples are presented which demonstrate that high order(More)
One of the conditions in the Kreiss matrix theorem involves the resolvent of the matrices A under consideration. This so-called resolvent condition is known to imply, for all n ≥ 1, the upper bounds ‖An‖ ≤ eK(N + 1) and ‖An‖ ≤ eK(n + 1). Here ‖ · ‖ is the spectral norm, K is the constant occurring in the resolvent condition, and the order of A is equal to N(More)
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