An exponentially fitted eighth-order method for the numerical solution of the Schrödinger equation

摘要

An eighth algebraic order exponentially fitted method is developed for the numerical integration of the Schrödinger equation. The formula considered contains certain free parameters which allow it to be fitted automatically to exponential functions. An comparative error analysis is also given. Numerical and theoretical results indicate that the new method is much more efficient than other classical and exponentially fitted methods.