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Error analysis of splitting methods for the time dependent Schrödinger equation

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Fig. 1. Graphs of |φ(my)/(my) − 1| (top) and #E(my)# (bottom) for some of the m-stage splitting methods collected in Table 1 and the 12th order scheme GM12
Fig. 2. Error, #y − y ap #, versus m (the degree of the Lanczos or Chebyshev polynomials or the number of stages for the splitting methods, leading to similar computational cost in all cases) for approximations to y = e −iA v, where v is chosen as a random
Fig. 3. Evolution of |ψ(x, t)| 2 for the solution corresponding to the P¨ oschl–Teller potential at t = 0, 2T, 4T .
Fig. 4. Error in time integration (solid lines), error bounds from (29) (dotted lines) for methods (30, 6, 1.4) and (30, 0, 1), and the spatial error (dashed lines) along the interval t ∈ [0, 128 T ] for the P¨ oschl–Teller potential

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