On parametric representation of the solution to differential equation and its approximate evaluation (Q677724)

This article will deal with certain modification of one-step numerical methods. It enables us to taken into account the maximal interval of existence of solution of problems \[ y'=f(x,y),\quad x\geq 0, \qquad y(0)=\alpha, \] and to bound it in order to exclude the groundless ``approximate solutions'' beyond this interval if it is finite. This modification is based on considering the solution as a curve on the plane \(Oxy\). It seems natural for such an approach to choose in the capacity of a step the length of the segment of the approximating curve contained between the points \((x_i,y_i)\) and \((x_{i+1},y_{i+1})\).