Iterative splitting methods for differential equations

Geiser presents a set of iterative operator splitting techniques for solving time-dependent equations, designed to make careful use of both processing power and memory. The main focus is on parabolic and hyperbolic systems, such as convection-diffusion-reaction problems, heat conduction, and wave motion.

The opening chapters are theoretical, establishing stability and consistency results for ordinary differential equations. The discussion then moves outward to partial differential equations and to models whose coefficients depend on space and time, showing how the same iterative approach carries over.

Later sections apply these methods to benchmark cases and real-world situations, including waste disposal, the propagation of elastic waves, and intricate fluid flows. Throughout, the book considers how splitting a complicated equation into simpler parts can help, and it treats multiphysics and multiscale problems as central themes. The text closes by reviewing software tools, namely r3t and FIDOS.