Теория массового обслуживания. Сивохин А.В - 257 стр.

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257
d
dt
p
0
t( ) = -5.08 p
0
t( ) + 4.12 p
1
t(), p
0
0( ) = 1.0,
d
dt
p
8
t( ) = -5.08 p
7
t( ) - 25.68 p
8
t( ) + 20.60 p
9
t()
?
?
?
> Runge_Kutt:=dsolve(ODESystemInit, numeric,
method=rkf45, {seq(p[i](t), i=0..n+m)});
Runge_Kutt := proc x_rkf45() ... end proc;
> Lpi[0]:=Runge_Kutt(0.0);
Lpi
0
:= [t = 0., p
0
t( ) = 1., p
1
t( ) = 0., p
2
t( ) = 0., p
3
t( ) = 0., p
4
t( ) = 0., p
5
t( ) = 0., p
6
t( ) = 0., p
7
t( ) = 0., p
8
t( ) = 0.,
p
9
t( ) = 0., p
10
t( ) = 0., p
11
t( ) = 0., p
12
t( ) = 0., p
13
t( ) = 0., p
14
t( ) = 0., p
15
t( ) = 0.]
> add(rhs(Lpi[0][i]), i=2..n+m+2);
1.
> Lpi[1]:=Runge_Kutt(0.5);
Lpi
1
:= [t = 0.5, p
0
t( ) = 0.340947384189586922, p
1
t( ) = 0.366626886179718726,
p
2
t( ) = 0.196807062042040294, p
3
t( ) = 0.0699290478011730942, p
4
t( ) = 0.0179834659722008032,
p
5
t( ) = 0.00295588150009783082, p
6
t( ) = -0.000480990873217040981,
p
7
t( ) = 0.0000773441941606259012, p
8
t( ) = -0.0000122644723314732769,
p
9
t( ) = 0.00000191330319118644698, p
10
t( ) = -2.92912808353403655 10
-7
,
p
11
t( ) = 4.38881221022720962 10
-8
, p
12
t( ) = -6.42573790315836824 10
-9
,
p
13
t( ) = 9.03785932107027134 10
-10
, p
14
t( ) = -1.48150907382263930 10
-10
,
p
15
t( ) = -2.43300666822969274 10
-11
]
> add(rhs(Lpi[1][i]), i=2..n+m+2);
0.9948354752
> Lpi[2]:=Runge_Kutt(1.0);
Lpi
2
:= [t = 1.0, p
0
t( ) = 0.295555169740299606, p
1
t( ) = 0.356915981783103964,
p
2
t( ) = 0.214376264893024276, p
3
t( ) = 0.0845571460412643944, p
4
t( ) = 0.0237296250396139066,
p
5
t( ) = 0.00410461572663643401, p
6
t( ) = -0.000709427321138331310,
p
7
t( ) = 0.000122501200062002404, p
8
t( ) = -0.0000211302213552323575,
p
9
t( ) = 0.00000364013634128291335, p
10
t( ) = -6.26218786206192592 10
-7
,
p
11
t( ) = 1.07476895817019282 10
-7
, p
12
t( ) = -1.85113579143996556 10
-8
,
p
13
t( ) = 3.02999874618722191 10
-9
, p
14
t( ) = -7.15369298826214752 10
-10
,
p
15
t( ) = -1.68954304840626148 10
-10
]
> add(rhs(Lpi[2][i]), i=2..n+m+2); 
         d                                                 d                                                 ?
            p0(t) = -5.08 p0(t) + 4.12 p1(t), p0(0) = 1.0,    p8(t) = -5.08 p7(t) - 25.68 p8(t) + 20.60 p9(t)?
         dt                                                dt                                                ?

> Runge_Kutt:=dsolve(ODESystemInit, numeric,
method=rkf45, {seq(p[i](t), i=0..n+m)});
                                         Runge_Kutt := proc(x_rkf45) ... end proc;

>    Lpi[0]:=Runge_Kutt(0.0);
    Lpi0 := [t = 0., p0(t) = 1., p1(t) = 0., p2(t) = 0., p3(t) = 0., p4(t) = 0., p5(t) = 0., p6(t) = 0., p7(t) = 0., p8(t) = 0.,

           p9(t) = 0., p10(t) = 0., p11(t) = 0., p12(t) = 0., p13(t) = 0., p14(t) = 0., p15(t) = 0.]


>    add(rhs(Lpi[0][i]), i=2..n+m+2);
                                                                  1.

>    Lpi[1]:=Runge_Kutt(0.5);
    Lpi1 := [t = 0.5, p0(t) = 0.340947384189586922, p1(t) = 0.366626886179718726,

           p2(t) = 0.196807062042040294, p3(t) = 0.0699290478011730942, p4(t) = 0.0179834659722008032,

           p5(t) = 0.00295588150009783082, p6(t) = -0.000480990873217040981,

           p7(t) = 0.0000773441941606259012, p8(t) = -0.0000122644723314732769,

                                                                                                 -7
           p9(t) = 0.00000191330319118644698, p10(t) = -2.92912808353403655 10 ,

                                                   -8                                          -9
           p11(t) = 4.38881221022720962 10 , p12(t) = -6.42573790315836824 10 ,

                                                   -10                                          -10
           p13(t) = 9.03785932107027134 10              , p14(t) = -1.48150907382263930 10              ,

                                                    -11
           p15(t) = -2.43300666822969274 10              ]


>    add(rhs(Lpi[1][i]), i=2..n+m+2);
                                                             0.9948354752

>    Lpi[2]:=Runge_Kutt(1.0);
    Lpi2 := [t = 1.0, p0(t) = 0.295555169740299606, p1(t) = 0.356915981783103964,

           p2(t) = 0.214376264893024276, p3(t) = 0.0845571460412643944, p4(t) = 0.0237296250396139066,

           p5(t) = 0.00410461572663643401, p6(t) = -0.000709427321138331310,

           p7(t) = 0.000122501200062002404, p8(t) = -0.0000211302213552323575,

                                                                                                 -7
           p9(t) = 0.00000364013634128291335, p10(t) = -6.26218786206192592 10 ,

                                                   -7                                          -8
           p11(t) = 1.07476895817019282 10 , p12(t) = -1.85113579143996556 10 ,

                                                   -9                                          -10
           p13(t) = 3.02999874618722191 10 , p14(t) = -7.15369298826214752 10                       ,

                                                    -10
           p15(t) = -1.68954304840626148 10              ]


>    add(rhs(Lpi[2][i]), i=2..n+m+2);
                                                                 257

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