Calculations of Singularities for Solutions of Algebraic Differential Equations

Abstract

In this introduction we first define nonlinear splines and describe their application to the solution of initial value problems of ordinary differential equations. Stability and convergence results for polynomial splines and their generalization to nonlinear splines are given. The Painleve theory is referred to for the motivation of the selection of nonlinear spline families in order to integrate the differential equations in the neigborhood of movable singularities of their solution. For two special cases the asymptotic behaviour of the estimation of the location of the singularity is analysed.