Introduction Model Problems Related Models for Decomposition Examples in Real-Life Applications Iterative Decomposition of Ordinary Differential Equations Historical Overview Decomposition Ideas Introduction to Classical Splitting Methods Iterative Splitting Method Consistency Analysis of the Iterative Splitting Method Stability Analysis of the Iterative Splitting Method for Bounded Operators Decomposition Methods for Partial Differential Equations Iterative Schemes for Unbounded Operators Computation of the Iterative Splitting Methods: Algorithmic Part Exponential Runge-Kutta Methods to Compute Iterative Splitting Schemes Matrix Exponentials to Compute Iterative Splitting Schemes Algorithms Extensions of Iterative Splitting Schemes Embedded Spatial Discretization Methods Domain Decomposition Methods Based on Iterative Operator Splitting Methods Successive Approximation for Time-Dependent Operators Numerical Experiments Introduction Benchmark Problems 1: Introduction Benchmark Problems 2: Comparison with Standard Splitting Methods Benchmark Problems 3: Extensions to Iterative Splitting Methods Real-Life Applications Conclusion to Numerical Experiments: Discussion of Some Delicate Problems Summary and Perspectives Software Tools Software Package Unstructured Grids Software Package r3t Solving PDEs Using FIDOS Appendix Bibliography Index.