Superstable two-step methods for the numerical integration of general second order initial value problems
The paper presents a class of two-step fourth order methods for the numerical integration of the general second order initial value problem. These methods are implicit and need an iterative process at each step. The author proves that the considered methods are superstable for the test equation \(y''+2\alpha y'+\beta^ 2y=0\), \(\alpha,\beta >0\), \(\alpha +\beta >0\). Such a kind of equation occurs, for example, in the numerical integration of singular perturbation problems. In my opinion more studies should be done on the practical application of these new methods. First of all it refers to the comparison of the methods proposed by the author with the other well-known methods for solving the general second order initial value problem. In this paper the author does not present any numerical examples.
scientific article; zbMATH DE number 3928242