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46) . 47) 0. Because of our assumptions, A is a generator of the one-parameter C0 semigroup (exp At)t≥0 . 47) with homogeneous initial conditions can be written as: t Ei (t) = tn exp(A(t − s))Fi (s)ds, t ∈ [tn , tn+1 ].

Numerical experiments can be done with physical parameters. Earthquake simulations motivate the study of elastic wave propagation. Realistic earthquake sources and a complex 3D earth structure are immensely important for understanding earthquake formation. A fundamental model of ground motion in urban sedimentary basins is studied and 3D software packages are developed, see [37] and [38]. , three-dimensional geology, propagating sources, and frequencies approaching 1 Hz) to be of engineering interest.

When the operators commute, then the method is exact. Hence, by definition, sequential operator splitting is called a first-order splitting method. 4. A characteristic of traditional splitting methods is the relation between the commutator and the consistency of the method, see references [20], and [56]. 20), where A and B are bounded operators in a Banach space X. 23) = 2 where [A, B] = 0 (0 is the zero matrix) if the operators do not commute. Based on the commutator [A, B], we have a large constant in the local splitting error of O(τn2 ) and therefore we have to use unrealistically small time steps, [82].

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