A FAMILY OF ITERATIVE METHODS IN THE THEORY OF MATHEMATICAL MODELLING

Abstract

Two types of recent iterative modelling methods are discussed. The first of them is based upon the theory of generalized integro-differential operators and applies to systems satisfying some kind of linear (ordinary or partial) differential equation. It seems to be useful, however, rather from theoretical than from practical point of view. The other procedure has a completely different character: it can be considered as a strong extension of the well-known logarithmization method combined with least squares adjustment, and leads to the analytical modelling of a lot of physical, engineering and biomedical systems or phenomena which could be described only empirically up to the present. Some ideas of the results have been published by the author e.g. in: Lecture Notes in Mathematics. 457 (Springer, 1975) as well as in the volume ":Mathematical Modelling in Science and Technology" (Pergamon Press. 1984).