This monograph is devoted to a study of iterative splitting methods for evolution equations that are systems of parabolic and hyperbolic equations with focus on convection-diffusion-reaction equations, heat equations and wave equations, which are used in the modelling of transport-reaction, heat transfer and elastic wave propagation. Theoretical and practical aspects of iterative splitting methods, used as decomposition methods, in time and space for evolution equations are described.
The author projects the following as the contributions made in this monograph.

1.

Consistency and stability results for linear operators (given in ordinary differential or spatially described partial differential equations).

2.

Acceleration of solver processes by decoupling of the full equation into simpler equations.

3.

Effectiveness of decomposed methods with respect to computational time and memory.

4.

Theory that is based on the standard splitting analysis and can be simply extended to more general cases, e.g., time dependent and spatial dependent.

5.

Embedding of higher-order time discretization methods in decoupled equations.

6.

Applications in computational sciences, e.g., flow problems, elastic wave propagation, and heat transfer.

7.

Splitting methods can also be used to couple equations, for example partial and ordinary differential equations or continuum and discrete model equations.

Two of the main contributions to the decomposition methods presented here are the attainment of higher-order accuracy and the incorporation of coupling techniques in solving real-life problems. A fairly complete bibliography consisting of 204 references is given at the end of the monograph, which includes several references to the works of the author (e.g., [Iterative operator-splitting methods for nonlinear differential equations and applications, numerical methods for partial differential equations, John Wily & Sons Ltd., West Sussex, UK, published online, March, (2010)]).