流动非线性及其同伦分析

所属分类:力学  
出版时间:2012-8   出版时间:高等教育出版社   作者:(美)瓦捷拉维鲁,(美)隔德 著   页数:190   字数:280000  

内容概要

  科学工程中的很多问题是非线性的,难以解决。传统的解析近似方法只对弱非线性问题有效,但无法很好地解决强非线性问题。同伦分析方法是近20年发展起来的一种有效的求解强非线性问题的解析近似方法。《流动非线性及其同伦分析:流体力学和传热(英文版)》介绍了同伦分析方法的最新理论进展,但不局限于方法的理论架构,也给出了大量的流体力学和传热中的非线性问题实例,来体现同伦分析方法的应用性。  《流动非线性及其同伦分析:流体力学和传热(英文版)》适合于物理、应用数学、非线性力学、金融和工程等领域对强非线性问题解析近似解感兴趣的科研人员和研究生。

作者简介

作者:(美国)瓦捷拉维鲁( Kuppalapalle Vajravelu) (美国)隔德(Robert A.Van Gorder)  瓦捷拉维鲁,为美国中佛罗里达大学数学系教授,机械、材料与航空和航天工程教授,Differential Equations and Nonlinear Mechanics的创刊主编。 隔德,任职于美国中佛罗里达大学。

书籍目录

1 Introduction
References
2  Principles of Homotopy Analysis
 2.1 Principles of homotopy and the homotopy analysis method
 2.2 Construction of the deformation equations
 2.3 Construction of the series solution
 2.4 Conditions for the convergence of the series solutions
 2.5 Existence and uniqueness of solutions obtained by
homotopyanalysis
 2.6 Relations between the homotopy analysis method and
otheranalytical methods
 2.7 Homotopy analysis method for the Swift-Hohenberg
equation
  2.7.1 Application of the homotopy analysis.method
  2.7.2 Convergence of the series solution and discussion of
results
 2.8 Incompressible viscous conducting fluid approaching a
permeable stretching surface
  2.8.1 Exact solutions for some special cases
  2.8.2 The case of G 0
  2.8.3 The case of G = 0
  2.8.4 Numerical solutions and discussion of the results
 2.9 Hydromagnetic stagnation point flow of a second grade fluid
over
  a stretching sheet
  2.9.1 Formulation of the mathematical problem
  2.9.2 Exact solutions
  2.9.3 Constructing analytical solutions via homotopy
analysis
References
……

章节摘录

版权页:
插图:
Thus,
while
arbitrary
functions
H
(x)
which
vanish
over
portions
of
the
relevantdomain
are
not
useful
in
the
homotopy
analysis
method,
one
has
the
option
to
employ
such
functions
provided
they
only
vanish
over
a
set
of
measure
zero.
One
maylook
at
this
in
another
way.
In
the
homotopy
given
in
(3.22),
we
introduce
the
newauxiliary
operator
(3.23)
which
depends
on
1/H
(x).
If
we
do
the
same
here,
we
seethat
if
H
(x)
vanishes
over
a
set
of
measure
zero,
then
the
auxiliary
linear
operatorconstructed
via
(3.23)
will
have
singularities
at
all
members
of
this
set
of
measurezero.
Such
singularities
greatly
complicate
the
problem
of
solving
the
linear
operator
to
obtain
the
terms
gm
(x)
in
the
mth
order
deformation
equations.
In
practice,these
vanishing
auxiliary
functions
will
modify
the
particular
solutions
obtainedwhen
solving
for
the
gm
(X)'S,
which
may
complicate
the
recursive
solution
process.As
such,
it
is
usually
best
to
avoid
auxiliary
functions
H
(x)
which
vanish
at
anypoint
over
the
domain
of
the
problem,
unless
one
has
a
good
reason
to
use
them.
Yet,
if
we
are
to
avoid
all
such
H
(x)
which
vanish
over
any
portion
of
the
domain,
we
can
just
as
well
elect
to
solve
the
modified
homotopy
(3.22)
using
themodified
auxiliary
linear
operator
(3.23).
This
is
why,
in
many
cases,
one
simplytakes
H
(x)
=
1
and
then
attempts
to
obtain
the
appropriate
initial
guess
and
auxiliary
linear
operator.
In
those
cases
where
a
different,
yet
nonvanishing
auxiliaryfunction
is
used,
one
may
simply
modify
the
auxiliary
linear
operator
to
arrive
atthe
same
results
(i.e.,
the
same
series
solutions).
However,
one
should
point
out
that
the
solution
expression
is
determined
by
thechoice
of
auxiliary
linear
operator,
L,
the
initial
approximation
and
the
functionH
(x).
When
one
does
not
know,
a
priori,
the
expression
of
solution,
then
one
cansimply
choose
H
(x)
=
1.
However,
we
should
point
out
that
simple
and
elegant
solutions
may
be
obtained
in
many
cases
by
properly
choosing
an
appropriate
functionalform
for
H
(x)
=
1.
3.3
Selection
of
the
convergence
control
parameter
The
convergence
control
parameter,
h

0,
was
introduced
by
Liao
in
order
to
control
the
manner
of
convergence
in
the
series
solutions
obtained
via
homotopy
analysis.
As
a
consequence,
once
the
initial
approximation,
auxiliary
linear
operator,and
auxiliary
function
are
selected,
the
homotopy
analysis
method
still
provides
onewith
a
family
of
solutions,
dependent
upon
the
convergence
control
parameter.
Sincewe
are
free
to
select
a
member
of
this
family
as
the
approximate
solution
to
a
nonlinear
equation,
we
find
that
the
convergence
region
and
the
convergence
rate
of
theseries
solutions
obtained
via
the
homotopy
analysis
method
depend
on
the
convergence
control
parameter.
As
a
consequence,
we
are
free
to
enhance
the
convergenceregion
and
the
convergence
rate
of
a
series
solution
via
an
appropriate
choice
of
theconvergence
control
parameter
h
even
for
fixed
choices
of
the
initial
approximation,auxiliary
linear
operator,
and
auxiliary
function.
Such
a
property
makes
the
homotopy
analysis
method
unique
among
analytical
techniques
and
provides
us
with
avery
powerful
tool
to
study
nonlinear
differential
equations.

编辑推荐

《流动非线性及其同伦分析:流体力学和传热(英文版)》适合于物理、应用数学、非线性力学、金融和工程等领域对强非线性问题解析近似解感兴趣的科研人员和研究生。

图书封面


    流动非线性及其同伦分析下载



用户评论 (总计2条)

 
 

  •     用英文写得,建议英语水平高的同学阅读,采用新的方法进行了分析,数学功底也有要求。但是适于科研人员参考借鉴。
  •     最近在学习HAM方法,感觉此书为很好的参考书。
 

自然科学类PDF下载,力学PDF下载。 PPT下载网 

PPT下载网 @ 2017