-
537
378.4 MATLAB
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e-mail:[email protected]
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. 2- . 3- . 1- (7 ) -
. 2- (3 ) (). , , . 3- (4 ) Partial Differential Equation
Toolbox. . , , . , PDE Toolbox, , , . .
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538
1. , .
1
. , , .. .
),( txu x t ),( xO .
lx 0 , ;0),(;0),0( == tlutu (1)
0=t .
=
=
=
)(),(
);()0,(
0
xvt
txuxxu
t
(2)
(1), (2)
],0[],0[);,(),(),(
2
2
2
2
TlDtxfx
txu
t
txu =+
=
(3)
.
],0[],0[);cos(sin)1(),(),( 2
2
2
2
2
TDxxx
txu
t
txu ==
(4)
;0;sin)0,(0
==
=tt
uxxu
(5)
() xxxu sin)()0,( ==
.
;0),(;0),0( == tutu (6)
)cos(sin),( txtxu = ( 2)cos( =t )
2=t .
5.0= , 4=t .
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539
2 u(x,t)
3 u(0,t)= u(l,t)=0
4 = 4
( 1=k ) )sin()1(:, xu = .
( NtkNxiutxutxu kiki ,2;1,2;),(),( , === )
kikikikikikiki f
h
uuuuuu,2
,1,,12
1,,1, 22 ++
=+ ++
, 0=
tt
u.
);1(:,1,2, vuu ii +=
1, +kiu Ntk ,2= .
kikikikikikiki fuuuhuuu ,
2,1,,12
2
1,,1, )2(2 +++= ++
%
%stringExplicit.m- (tau/h)
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540
u(:,1)=sin(x(:));v(:,1)=0; title('
'); xlabel('x');ylabel('t');zlabel('u')
. (4) (6)
],0[],0[;0),(),(
2
2
2
2
TDx
txu
t
txu ==
;0;sin)0,(0
==
=tt
uxxu ;0),(;0),0( == tutu
, txtxu cossin),(~ = . txtxu cossin),(~ = - , 1= - . 3-D
, 1= .
),( txf , 1= , txtxf cossin),( = . ]24,0[ t .
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541
. ;05.0;1.0 ==h .. 0.5;=
h
1
