Optimal stability polynomials for splitting methods, with application to the time-dependent Schrödinger equation
The authors determine optimal stability polynomials for the splitting method to solve systems of ordinary differential equations, accurate to the eighth order in the time step. The method is applied to the construction of symplectic corrector algorithms which approximate the solutions of linear Hamiltonian systems. As an illustration, the authors examine the discretized form of the time-dependent Schrödinger equation which can be reduced to a Hamiltonian system and describes the time evolution of a particle in a certain one-dimensional potential.
scientific article; zbMATH DE number 1088834
scientific article