A mono-implicit Runge-Kutta-Nyström modification of the Numerov method

We present two two-parameter families of fourth-order mono-implicit Runge-Kutta-Nystrom methods. Each member of these families can be considered as a modification of the Numerov method. We analyze the stability and periodicity properties of these methods. It is shown that (i) within one of these families there exist A-stable (even L-stable) and P-stable methods, and (ii) in both families there exist methods with a phase lag of order six

Biconic semi-copulas with a given section

Inspired by the notion of biconic semi-copulas, we introduce biconic semi-copulas with a given section. Such semi-copulas are constructed by linear interpolation on segments connecting the graph of a continuous and decreasing function to the points (0, 0) and (1, 1). Special classes of biconic semi-copulas with a given section such as biconic (quasi-)copulas with a given section are considered. Some examples are also provided

Properties and implementation of r-Adams methods based on mixed-type interpolation

We investigate the properties of the coefficients of modified r-Adams methods for the integration of ODEs. The derivation of these methods is, in contrast with the classical Adams methods, not based on a polynomial interpolation theory, but rather starts from a mixed interpolation theory in which a parameter kappa is involved. It will be shown that the coefficients of the modified methods possess properties which make these methods very attractive. Further, we will discuss the role of so-called over-implicit modified r-Adams schemes in the construction of more general linear multistep methods. Our second goal is to show that the modified Adams-Bashforth/Adams-Moulton methods are very well suited to be implemented as a predictor-corrector pair. In particular, are will discuss the choice of the interpolation parameter when such a method is applied to general systems of equations. Numerical tests are performed to support the theory