Теория массового обслуживания. Сивохин А.В - 156 стр.

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156
вероятностей состояний pi(t) методом Рунге-Кутта
> Runge_Kutt:=dsolve(ODESystemInit, numeric,
method=rkf45, {p[1](t), p[2](t), p[3](t),
p[4](t)});
Runge_Kutt := proc x_rkf45() ... end proc;
> Lpi[0]:=Runge_Kutt(0.0);
Lpi
0
:= [t = 0., p
1
t( ) = 0.20000000000000, p
2
t( ) = 0.25000000000000, p
3
t( ) = 0.30000000000000,
p
4
t( ) = 0.25000000000000]
> Lpi[1]:=Runge_Kutt(0.5);
Lpi
1
:= [t = 0.5, p
1
t( ) = 0.208159368177884356, p
2
t( ) = 0.462453057932644296,
p
3
t( ) = 0.169798252349092820, p
4
t( ) = 0.159589321540378582]
> Lpi[2]:=Runge_Kutt(1.0);
Lpi
2
:= [t = 1.0, p
1
t( ) = 0.206237520248503698, p
2
t( ) = 0.464519383234870854,
p
3
t( ) = 0.167451502727404416, p
4
t( ) = 0.161791593789221144]
> Lpi[3]:=Runge_Kutt(1.5);
Lpi
3
:= [t = 1.5, p
1
t( ) = 0.206148128226249062, p
2
t( ) = 0.464564402243090758,
p
3
t( ) = 0.167405049239433030, p
4
t( ) = 0.161882420291227264]
> Lpi[4]:=Runge_Kutt(2.0);
Lpi
4
:= [t = 2.0, p
1
t( ) = 0.206145055803345940, p
2
t( ) = 0.464565817650475944,
p
3
t( ) = 0.167403682259746888, p
4
t( ) = 0.161885444286431201]
> Lpi[5]:=Runge_Kutt(5.0);
Lpi
5
:= [t = 5.0, p
1
t( ) = 0.206144858033232458, p
2
t( ) = 0.464565825973056846,
p
3
t( ) = 0.167403802375170968, p
4
t( ) = 0.161885513618540089]
> Lpi[6]:=Runge_Kutt(10.0);
Lpi
6
:= [t = 10.0, p
1
t( ) = 0.206144943215032516, p
2
t( ) = 0.464565837564750728,
p
3
t( ) = 0.167403683788543978, p
4
t( ) = 0.161885535431672806]
> Lpi[7]:=Runge_Kutt(20.0);
Lpi
7
:= [t = 20.0, p
1
t( ) = 0.206145057963146860, p
2
t( ) = 0.464565857509935398,
p
3
t( ) = 0.167403525050387720, p
4
t( ) = 0.161885559476530882]
> Lp1:=[seq(rhs(Lpi[t][2]), t=0..7)];
Lp1 := [0.20000000000000, 0.208159368177884356, 0.206237520248503698, 0.206148128226249062, 
вероятностей состояний pi(t) методом Рунге-Кутта

> Runge_Kutt:=dsolve(ODESystemInit, numeric,
method=rkf45, {p[1](t), p[2](t), p[3](t),
p[4](t)});
                                  Runge_Kutt := proc(x_rkf45) ... end proc;

>   Lpi[0]:=Runge_Kutt(0.0);
        Lpi0 := [t = 0., p1(t) = 0.20000000000000, p2(t) = 0.25000000000000, p3(t) = 0.30000000000000,

             p4(t) = 0.25000000000000]


>   Lpi[1]:=Runge_Kutt(0.5);
               Lpi1 := [t = 0.5, p1(t) = 0.208159368177884356, p2(t) = 0.462453057932644296,

                     p3(t) = 0.169798252349092820, p4(t) = 0.159589321540378582]


>   Lpi[2]:=Runge_Kutt(1.0);
               Lpi2 := [t = 1.0, p1(t) = 0.206237520248503698, p2(t) = 0.464519383234870854,

                     p3(t) = 0.167451502727404416, p4(t) = 0.161791593789221144]


>   Lpi[3]:=Runge_Kutt(1.5);
               Lpi3 := [t = 1.5, p1(t) = 0.206148128226249062, p2(t) = 0.464564402243090758,

                     p3(t) = 0.167405049239433030, p4(t) = 0.161882420291227264]


>   Lpi[4]:=Runge_Kutt(2.0);
               Lpi4 := [t = 2.0, p1(t) = 0.206145055803345940, p2(t) = 0.464565817650475944,

                     p3(t) = 0.167403682259746888, p4(t) = 0.161885444286431201]


>   Lpi[5]:=Runge_Kutt(5.0);
               Lpi5 := [t = 5.0, p1(t) = 0.206144858033232458, p2(t) = 0.464565825973056846,

                     p3(t) = 0.167403802375170968, p4(t) = 0.161885513618540089]


>   Lpi[6]:=Runge_Kutt(10.0);
               Lpi6 := [t = 10.0, p1(t) = 0.206144943215032516, p2(t) = 0.464565837564750728,

                     p3(t) = 0.167403683788543978, p4(t) = 0.161885535431672806]


>   Lpi[7]:=Runge_Kutt(20.0);
               Lpi7 := [t = 20.0, p1(t) = 0.206145057963146860, p2(t) = 0.464565857509935398,

                     p3(t) = 0.167403525050387720, p4(t) = 0.161885559476530882]


>   Lp1:=[seq(rhs(Lpi[t][2]), t=0..7)];
    Lp1 := [0.20000000000000, 0.208159368177884356, 0.206237520248503698, 0.206148128226249062,

                                                     156

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