Predictor-corrector (PC) methods for the numerical solution of stiff ODEs can be extended to include the second derivative of the solution. In this paper, we consider second derivative PC methods with the three-step second derivative Adams-Bashforth as predictor and two-step second derivative Adams-Moulton as corrector which both methods have order six. Implementation of the proposed PC method ...

We describe a construction of implicit two–step Runge–Kutta methods for ordinary differential equations in Nordsieck form and their continuous extensions. This representation allows accurate and reliable estimation of the local discretization errors and the application to differential equations with delays. Two stiffly accurate methods of order three with quadratic interpolants are derived, one...

Terrestrial and aquatic gastropods from the upper Eocene (Priabonian) Zalumah Formation in the Salalah region of the Sultanate of Oman are described. The assemblages reflect the composition of the continental mollusc fauna of the Palaeogene of Arabia, which, at that time, formed parts of the southeastern Tethys coast. Several similarities with European faunas are observed at the family level, b...

Hard processes at the TeV scale exhibit enhanced (double log) EW corrections even for inclusive observables, leading to violation of the Bloch-Nordsieck theorem. This effect, previously related to the non abelian nature of free EW charges in the initial state (ee, ep, pp ...), is here investigated for fermion initiated hard processes and to all orders in EW couplings. We find that the effect is...

For uniform meshes it is shown that any linear fc-step formula can be formulated so that only k values need to be saved between steps. By saving additional m values it is possible to construct local polynomial approximations of degree k + m — 1, which can be used as predictor formulas. Different polynomial bases lead to different equivalent forms of multistep formulas. In particular, local mono...