This volume introduces a unified, self-contained study of linear
discrete parabolic problems through reducing the starting discrete
problem to the Cauchy problem for an evolution equation in discrete
time. Accessible to beginning graduate students, the book contains
a general stability theory of discrete evolution equations in
Banach space and gives applications of this theory to the analysis
of various classes of modern discretization methods, among others,
Runge-Kutta and linear multistep methods as well as operator
splitting methods.
Key features:
* Presents a unified approach to examining discretization methods
for parabolic equations.
* Highlights a stability theory of discrete evolution equations
(discrete semigroups) in Banach space.
* Deals with both autonomous and non-autonomous equations as well
as with equations with memory.
* Offers a series of numerous well-posedness and convergence
results for various discretization methods as applied to abstract
parabolic equations; among others, Runge-Kutta and linear multistep
methods as well as certain operator splitting methods.
* Provides comments of results and historical remarks after each
chapter.
. Presents a unified approach to examining discretization methods
for parabolic equations.
. Highlights a stability theory of discrete evolution equations
(discrete semigroups) in Banach space.
. Deals with both autonomous and non-autonomous equations as well
as with equations with memory.
. Offers a series of numerous well-posedness and convergence
results for various discretization methods as applied to abstract
parabolic equations; among others, Runge-Kutta and linear multistep
methods as well as certain operator splitting methods as well as
certain operator splitting methods are studied in detail.
.Provides comments of results and historical remarks after each
chapter."
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