Padé – Type Integrators for Initial Value Problems

Abstract

A formal direct conversion of a general Padé Approximant into its corresponding general rational integrator is made through the use of a real
operator and its power series. The research work proved that the derived integrators are consistent and convergent. Experiments carried out reveal that the polynomial degree of the numerator and denominator can be chosen freely. Results of our experiments also indicate good performance of the integrators on the selected problems.

Keywords: Power series, Padé-Type integrators, underlying interpolants, zero entries, linear algebraic equations.