The Symplectic Splitting Method

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The Taylor Method An m-stage Taylor method to approximate where is the Taylor expansion of the exponential, which approximates the exact solution up to order m
The Taylor Method An m-stage Taylor method to approximate where is the Taylor expansion of the exponential, which approximates the exact solution up to order m We can advance each step by using the Horner's algorithm This algorithm can be trivially rewritten in terms of the real vectors, and it only requires to store two extra complex vectors (four real vectors).
Page 1 and 2: Splitting and composition methods f
Page 3 and 4: The Methods Considered I - If the s
Page 5: The Methods Considered I - If the s
Page 9 and 10: The Chebyshev Method The Chebyshev
Page 11 and 12: Taylor order tol=inf tol=10 -8 tol=
Page 13 and 14: The linear time dependent SE with H
Page 15 and 16: The Symplectic Splitting Method The
Page 17 and 18: Error bounds: Splitting Methods: va
Page 19 and 20: LOG(ERROR) 0 -2 -4 -6 -8 -10 -12 Po
Page 21 and 22: LOG(ERROR) 0 -2 -4 -6 -8 -10 -12 Po
Page 23 and 24: References SB, F. Casas, and A. Mur
Page 25 and 26: Splitting methods with complex coef
Page 27 and 28: Splitting methods with complex coef
Page 29 and 30: Splitting for perturbed systems Add
Page 31 and 32: Splitting for perturbed systems Add

The Symplectic Splitting Method

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