Preface Introduction Modeling: Multi-Physics Problems Introduction Models for Multi-Physics Problems Examples for Multi-Physics Problems Abstract Decomposition and Discretization Methods Decomposition Discretization Time-Decomposition Methods for Parabolic Equations Introduction for the Splitting Methods Iterative Operator-Splitting Methods for Bounded Operators Iterative Operator-Splitting Methods for Unbounded Operators Decomposition Methods for Hyperbolic Equations Introduction for the Splitting Methods ADI Methods and LOD Methods Iterative Operator-Splitting Methods for Wave Equations Parallelization of Time Decomposition Methods Nonlinear Iterative Operator-Splitting Methods Spatial Decomposition Methods Domain Decomposition Methods Based on Iterative Operator-Splitting Methods Schwarz Waveform-Relaxation Methods Overlapping Schwarz Waveform Relaxation for the Solution of Convection-Diffusion-Reaction Equation Numerical Experiments Introduction Benchmark Problems for the Time Decomposition Methods for Ordinary Differential and Parabolic Equations Benchmark Problems for Spatial Decomposition Methods: Schwarz Waveform-Relaxation Method Benchmark Problems: Hyperbolic Equations Real-Life Applications Summary and Perspectives Notation Appendix A: Software Tools Appendix B: Discretization Methods Literature References Index.