The Parker Sochacki Method of Taylor Series Generation With A-priori Error Estimates.

The Parker Sochacki Method or Power Series Method (PSM) is a simple, fast, powerful, and accurate method of solving systems of ordinary differential equations (ODE's). The system is broken down into unary and binary operations, everything is treated as a Taylor series, and series coefficients are equated. While popular interpolative methods, such as Runga-Kutta can miss narrow poles, the a-priori absolute error estimate of PSM locates all poles and provides domains of convergence. PSM can always be cast in polynomial form, which allows separation of variables in physical systems, facilitating exploration of hidden symmetries. PSM is implicitly symplectic.