A new symmetric linear eight-step method with fifth trigonometric order for the efficient integration of the Schrِdinger equation

On the basis of a classical symmetric eight-step method, an optimized method with fifth trigonometric order for the numerical solution of the Schrِdinger equation is developed in this work. The local truncation error analysis of the method proves the decrease of the maximum power of the energy in relation to the corresponding classical method, which renders the method highly efficient. This is confirmed by comparing the method to other methods from the literature while integrating the equation. The superiority of the method is strengthened by the existence of a larger interval of periodicity of the new method in comparison to the corresponding classical method.