By Juergen Geiser

**Read or Download Iterative Splitting Methods for Differential Equations (Chapman and Hall CRC Numerical Analysis and Scientific Computation Series) PDF**

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**Extra info for Iterative Splitting Methods for Differential Equations (Chapman and Hall CRC Numerical Analysis and Scientific Computation Series)**

**Example text**

These algorithms integrate each underlying equation with respect to the last iterated solution. Therefore, the starting solution in each iterative equation is important in order to guarantee fast convergence or a higher-order method. The last iterative solution should at least have a local error of O(τni ) (i-th order in time), where i is the number of iteration steps, to obtain the next higher order. We deal with at least two equations, therefore two operators, but the results can be generalized to n operators (see for example the ideas of waveformrelaxation methods [199]).

For this model, we propose the decomposition of ﬂow and reaction processes, which are given on diﬀerent time scales, and we are free to accelerate the solving process. 2 Elastic Wave Propagation In the second model, we simulate the propagation of elastic waves produced by earthquakes. Here, the motivation arises from predicting possible earthquake formation in a given scenario of earthquakes about the center. Therefore, the following conditions must be fulﬁlled: • A realistic model problem has to consider a singular forcing term.

Here the motivation came from applying the algorithms of time and space decomposition methods, see [64], [199]. Here especially waveform relaxation methods are used to solve ordinary and partial diﬀerential equations, see [139], [199]. , Parareal, see [65]. , diagonal matrices, see [199]. On the other hand, the methods can accelerate the solver process with parallelized algorithms, see [65]. The second origin is motivated more by solving transport reaction problems. Here, the algorithms are focused on solving each part separately to save on computational time, see [147].