homogeneous linear partial differential equations with constant coefficients
Tài liệu Báo cáo " Fully parallel methods for a class of linear partial differential-algebraic equations " pptx
Ngày tải lên :
13/02/2014, 03:20
... revised form 12 December 2007
Abstract. This note deals with two fully parallel methods for solving linear partial differential-
algebraic equations (PDAEs) of the form:
Au
t
+ B∆u = f(x, t) (1)
where ... Mathematics - Physics 23 (2007) 201-209
Fully parallel methods for a class of linear partial
differential- algebraic equations
Vu Tien Dung
∗
Department of Mathematics, Mechanics, Informatics, College ... Solution of Linear Parabolic Problems, Applied Mathematics Research Express No. 4
(2005) 117.
[5] R.D. da Cunha, T.R. Hopkins, Parallel Over Relaxation Algorithms for Systems of Linear Equations, ...
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Partial Differential Equations part 1
Ngày tải lên :
28/10/2013, 22:15
... America).
Chapter 19. Partial Differential
Equations
19.0 Introduction
The numerical treatment of partial differential equations is, by itself, a vast
subject. Partial differential equations are at ... Recipes dealing with partial differential equations alone. (The
references
[1-4]
provide, of course, available alternatives.)
In most mathematics books, partial differential equations (PDEs) ... the
solutionof large numbers of simultaneous algebraic equations. When such equations
are nonlinear, they are usually solved by linearization and iteration; so without much
loss of generality we can view...
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Partial Differential Equations part 2
Ngày tải lên :
07/11/2013, 19:15
... error is one associated with nonlinear hyperbolic equations and
is therefore sometimes called nonlinearinstability. For example, a piece of the Euler
or Navier-Stokes equations for fluid flow looks ... equation, the one-dimensional wave
equation with constant velocity of propagation v
∂
2
u
∂t
2
= v
2
∂
2
u
∂x
2
(19.1.2)
836
Chapter 19. Partial Differential Equations
Sample page from NUMERICAL RECIPES ... but
they do not work well for problems with discontinuities.
CITED REFERENCES AND FURTHER READING:
Ames, W.F. 1977,
Numerical Methods for Partial Differential Equations
, 2nd ed. (New York:
Academic...
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Tài liệu Partial Differential Equations part 3 pptx
Ngày tải lên :
15/12/2013, 04:15
... units so that Planck’s constant ¯h =1and the particle mass
m =1/2.) One is given the initial wavepacket, ψ(x, t =0), together with boundary
852
Chapter 19. Partial Differential Equations
Sample page ... write
D
j+1/2
=
1
2
D(u
n
j+1
)+D(u
n
j
)
(19.2.22)
Implicit schemes are not as easy. The replacement (19.2.22) with n → n +1leaves
us with a nasty set of coupled nonlinear equations to solve at each timestep. Often
there is an easier way: ... 848
Chapter 19. Partial Differential Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN...
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Tài liệu Partial Differential Equations part 4 ppt
Ngày tải lên :
15/12/2013, 04:15
... value problems (elliptic equations, for
example) reduce to solving large sparse linear systems of the form
A· u = b (19.4.1)
either once, for boundary value equations that are linear, or iteratively, ... ∆t)
u
n+(2/m)
= U
2
(u
n+(1/m)
, ∆t)
···
u
n+1
= U
m
(u
n+(m−1)/m
, ∆t)
(19.3.20)
854
Chapter 19. Partial Differential Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... once again!
CITED REFERENCES AND FURTHER READING:
Ames, W.F. 1977,
Numerical Methods for Partial Differential Equations
, 2nd ed. (New York:
Academic Press), Chapter 2.
Goldberg, A., Schey, H.M.,...
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Tài liệu Partial Differential Equations part 5 ppt
Ngày tải lên :
15/12/2013, 04:15
... systems.
In practice, equations (19.4.33) should be rewritten to avoid numerical instabil-
ity. For these and other practical details, refer to
[2]
.
860
Chapter 19. Partial Differential Equations
Sample ... problems (elliptic equations, for
example) reduce to solving large sparse linear systems of the form
A · u = b (19.4.1)
either once, for boundary value equations that are linear, or iteratively, ... FACR with r =0(that is, FFT in one dimension and solve the
tridiagonal equations by the usual algorithm in the other dimension) gives about a
factor of two gain in speed. The optimal FACR with...
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Tài liệu Partial Differential Equations part 6 doc
Ngày tải lên :
15/12/2013, 04:15
... multigrid methods can solve general
elliptic equations with nonconstant coefficients with hardly any loss in efficiency.
Even nonlinear equations can be solved with comparable speed.
Unfortunately there ... the various components of the algorithm
within this framework to solve your specific problem. We can only give a brief
868
Chapter 19. Partial Differential Equations
Sample page from NUMERICAL RECIPES ... FACR with r =0(that is, FFT in one dimension and solve the
tridiagonal equations by the usual algorithm in the other dimension) gives about a
factor of two gain in speed. The optimal FACR with...
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- 0
Tài liệu Partial Differential Equations part 7 doc
Ngày tải lên :
24/12/2013, 12:16
... multigrid methods can solve general
elliptic equations with nonconstant coefficients with hardly any loss in efficiency.
Even nonlinear equations can be solved with comparable speed.
Unfortunately there ... the various components of the algorithm
within this framework to solve your specific problem. We can only give a brief
874
Chapter 19. Partial Differential Equations
Sample page from NUMERICAL RECIPES ... the
finest level. FMG needs f at all levels. If the boundary conditionsare homogeneous,
878
Chapter 19. Partial Differential Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC...
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Functional analysis sobolev spaces and partial differential equations
Ngày tải lên :
04/02/2014, 11:10
... elements from two distinct
“worlds”: functional analysis (FA) and partial differential equations (PDEs). The first
part deals with abstract results in FA and operator theory. The second part concerns
the ... range of questions, in both pure
and applied mathematics. They appear in linear and nonlinear PDEs that arise, for
example, in differential geometry, harmonic analysis, engineering, mechanics, and
physics. ... be a linear subspace. If g : G → R is a continuous
linear functional, then there exists f ∈ E
that extends g and such that
f
E
= sup
x∈G
x≤1
|g(x)|=g
G
.
Proof. Use Theorem 1.1 with...
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Tài liệu AN INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS ppt
Ngày tải lên :
16/02/2014, 15:20
... a webpage with a list of errata at http://www.math.technion.ac
.il/∼pincho/PDE.pdf.
AN INTRODUCTION TO PARTIAL DIFFERENTIAL
EQUATIONS
A complete introduction to partial differential equations, ... fourth-order equation.
r
Linear equations
Another classification is into two groups: linear versus nonlinear equations. An equation is
called linear if in (1.1), F is a linear function of the unknown ... assumed that the reader is familiar with the calculus of functions in several
variables, with linear algebra and with the basics of ordinary differential equations.
The book is almost entirely...
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