Introduction to the contents of issue 50:2

Abstract

I write this in the month of March, when skiers are still rushing down the slope outside my window and we celebrated the International Women’s Day on March 8. I note with appreciation that women are coming to prominence in our field of scientific endeavor. Of the 24 authors in this issue at least 8 are women, making it one of three. Last time I counted, issue 45:1, it was 6 of 25 or one of four. The share of women is expanding, let me guess that after another 5 years they will be one of two! Let me now present the contributions to this second issue of volume 50: Manuel Calvo, M. Pilar Laburta, J. Ignazio Montijano and Luis Randez describe a Runge Kutta method, applied to an autonomous initial value problem, which preserves a smooth Lyapunov function. This gives a new tool to compute a numerical solution that has the same regularity as the mathematical model. Gheorghe Coman and Teodora Catinas develop Lagrange, Hermite and Birkhoff interpolation operators over a triangle with one curved side. Such interpolations are useful to build up finite element approximations over nonstandard regions. Constanza Conti and Lucia Romani study how to subdivide an interval to make up spline approximations that converge to a wanted smooth function. The interest is on subdivisions with variable masks and shifted affine combinations of known symbols are used. Sergei Gusev, Stefan Johansson, Bo Kagstrom, Anton Shiriaev and Andras Varga describe and compare several algorithms to solve a periodic Riccati system of linear ordinary differential equations. Two of the algorithms are of a multiple shooting character, and rely upon finding a stable invariant subspace of an associated Hamiltonian