  A matrix inverse free method to solve time-dependent Schrodinger equation is
presented. The method is not subject to form of Hamiltonian and adopting real
space grid system such as structured and unstructured grid, and achieves the
order N algorithm even if we adopt unstructured grid systems to adjust complex
regions. We have demonstrated some error evaluation problems that have exact
solution and application in which it has non-Schrodinger type Hamiltonian, and
we have successfully simulated the time-evolution of wave function for all of
the case.
