Rational one-step methods for initial value problems (Q1114316)

The rational one-step methods discussed are based on Padé approximations to the Taylor series of the local solutions of the differential equation. The local increments in these schemes are represented as finite continued fractions: in this way the coefficients become independent of the order chosen. On the other hand, the schemes require some higher derivatives of the local solutions at the grid points. - Some numerical examples show that the rational methods are advantageous near a pole of the solutions and also in the case of a stiff system.