A. MONGELLI and S. NOSCHESE
Uniform polynomial approximation to solutions of the Cauchy problem for O.D.E.
Pages: 195-204
Received: 22 February 2000
Revised: 26 June 2000
Mathematics Subject Classification (2000): 63D15 - 65L05
Abstract: We show an analytical method, based on Chaplygin's differential Genera of reducible curves not contained in hypersurfaces of given degree inequalities theorem, for the construction of sequences of polynomials uniformly approaching the solution of the Cauchy problem for ordinary differential equations in the real line y' = f(x,y); y(x0) = y0, in a suitable neighborhood of the initial point x0.