An enhancement of transformation method

摘要

To solve Cauchy problem, for an ordinary second-order linear homogeneous differential equation, we use, so-called, transformation method. This numerical technique does not rely on expansion in Poincaré series, however, it requires integration of a nonlinear second-order ordinary differential equation. This formidable task substantially diminishes when instead of the nonlinear second-order equation we integrate a linear third-order equation.