Iterative Splitting Methods for Differential Equations explains
how to solve evolution equations via novel iterative-based
splitting methods that efficiently use computational and memory
resources. It focuses on systems of parabolic and hyperbolic
equations, including convection-diffusion-reaction equations, heat
equations, and wave equations.
In the theoretical part of the book, the author discusses the
main theorems and results of the stability and consistency analysis
for ordinary differential equations. He then presents extensions of
the iterative splitting methods to partial differential equations
and spatial- and time-dependent differential equations.
The practical part of the text applies the methods to benchmark
and real-life problems, such as waste disposal, elastics wave
propagation, and complex flow phenomena. The book also examines the
benefits of equation decomposition. It concludes with a discussion
on several useful software packages, including r3t and FIDOS.
Covering a wide range of theoretical and practical issues in
multiphysics and multiscale problems, this book explores the
benefits of using iterative splitting schemes to solve physical
problems. It illustrates how iterative operator splitting methods
are excellent decomposition methods for obtaining higher-order
accuracy.
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