On the Order of Operator Splitting Methods for Time-dependent Linear Systems of Differential Equations
نویسنده
چکیده
One way to solve complicated systems of differential equations is the application of operator splitting techniques. The original problem is split into several subsystems that are solved cyclically one after the other. Naturally, this procedure introduces an error, which is called splitting error, into the calculations. It is known that if the splitting procedure is applied to autonomous systems of ordinary differential equations, then the frequently used splitting procedures: the sequential, the Strang-Marchuk and the symmetrically weighted sequential splittings generally have splitting errors of order one and two, respectively. In this paper, we show that the order of the splitting procedures is preserved for non-autonomous problems. The theoretical results will be verified on numerical test problems.
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