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Applications of Lie groups to difference equations
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Description
Rating
Title
Applications
of
Lie
groups
to
difference
equations
Creator
Dorodnitsyn, V. A. (Vladimir Anatol'evich), 1947
DescriptionAbstract
Intended
for
researchers
,
numerical
analysts
, and
graduate
students
in
various
fields
of
applied
mathematics
,
physics
,
mechanics
, and
engineering
sciences
,
Applications
of
Lie
Groups
to
Difference
Equations
is
the
first
book
to
provide
a
systematic
construction
of
invariant
difference
schemes
for
nonlinear
differential
equations
. A
guide
to
methods
and
results
in a
new
area
of
application
of
Lie
groups
to
difference
equations
,
difference
meshes
(lattices)
, and
difference
functionals
, this
book
focuses
on the
preservation
of
complete
symmetry
of
original
differential
equations
in
numerical
schemes
. This
symmetry
preservation
results
in
symmetry
reduction
of the
difference
model
along
with that of the
original
partial
differential
equations
and in
order
reduction
for
ordinary
difference
equations.A
substantial
part
of the
book
is
concerned
with
conservation
laws
and
first
integrals
for
difference
models
. The
variational
approach
and
Noether
type
theorems
for
difference
equations
are
presented
in the
framework
of the
Lagrangian
and
Hamiltonian
formalism
for
difference
equations
. In
addition
, the
book
develops
difference
mesh
geometry
based
on a
symmetry
group
,
because
different
symmetries
are
shown
to
require
different
geometric
mesh
structures
. The
method
of
finitedifference
invariants
provides
the
mesh
generating
equation
, any
special
case
of
which
guarantees
the
mesh
invariance
. A
number
of
examples
of
invariant
meshes
is
presented
. In
particular
, and with
numerous
applications
in
numerics
for
continuous
media
, that
most
evolution
PDEs
need
to be
approximated
on
moving
meshes.Based
on the
developed
method
of
finitedifference
invariants
, the
practical
sections
of the
book
present
dozens
of
examples
of
invariant
schemes
and
meshes
for
physics
and
mechanics
. In
particular
, there are
new
examples
of
invariant
schemes
for
secondorder
ODEs
, for the
linear
and
nonlinear
heat
equation
with a
source
, and for
wellknown
equations
including
Burgers
equation
, the
KdV
equation
, and the
Schr??dinger
equationProvided
by
publisher.;""This
book
presents
a
survey
of
methods
and
results
in a
new
application
area
of
Lie
groups
to
difference
equations
and
difference
meshes
(lattices)
.
It
focuses
on the
formulation
and
mathematical
substantiation
of
exact
symmetry
preservation
in
difference
models
,
such
as
difference
equations
and
meshes
.
Methods
are
illustrated
with
numerous
examples
and
applications
in
heat
and
mass
transfer
,
hydrodynamics
,
physics
, and
mechanics
. To
highlight
the
numerical
aspect
of the
book
, the
author
provides
a
short
survey
of
methods
and
theory
of
finite
difference
schemes
and
meshes
. He also
explains
other
approaches
to
quality
features
of
difference
schemes
,
such
as
variational
and
moving
frames
methods""Provided
by
publisher
.
DescriptionTable Of Contents
1
.
Finite
differences
and
transformation
groups
in
space
of
discrete
variables

2
.
Invariance
of
finitedifference
models

3
.
Invariant
difference
models
of
ordinary
differential
equations

4
.
Invariant
difference
models
of
partial
differential
equations

5
.
Combined
mathematical
models
and
some
generalizations

6
.
Lagrangian
formalism
for
difference
equations

7
.
Hamiltonian
formalism
for
difference
equations
:
symmetries
and
first
integrals

8
.
Discrete
representation
of
ordinary
differential
equations
with
symmetries
.
Publisher
CRC Press
Subject
Difference equations
Identifier (Full text)
http://marc.crcnetbase.com/isbn/9781420083101
ISBN
9781420083101
(ebook)
Language
eng
Type
Text
FormatExtent
1 online resource (lxxx, 264 p.)
Date
2011
RelationIs Part Of
Differential and integral equations and their applications , v. 8.
Purchased by
Puey Ungphakorn Library, Rangsit Campus
OCLC number
989089822
CONTENTdm number
15167
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