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215
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d
dt
p
2
t()
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d
dt
p
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t()
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dt
p
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t()
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d
dt
p
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t()
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p
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t()
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t()
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p
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t()
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p
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t()
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dt
p
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t()
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d
dt
p
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t()
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d
dt
p
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t()
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dt
p
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t()
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dt
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t()
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dt
p
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t()
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, p
1
0( ) = 0., p
2
0( ) = 0., p
3
0( ) = 0., p
4
0( ) = 0.,
d
dt
p
8
t( ) = -5.08 p
7
t( ) - 44.07 p
8
t( ) + 45.12 p
9
t(),
d
dt
p
9
t( ) = -5.08 p
8
t( ) - 50.20 p
9
t( ) + 51.25 p
10
t(),
p
5
0( ) = 0., p
6
0( ) = 0., p
7
0( ) = 0., p
8
0( ) = 0., p
9
0( ) = 0.,
d
dt
p
10
t( ) = -5.08 p
9
t( ) - 56.33 p
10
t( ) + 57.38 p
11
t(), p
10
0( ) = 0., p
11
0( ) = 0., p
12
0( ) = 0., p
13
0( ) = 0.,
p
14
0( ) = 0., p
15
0( ) = 0., p
16
0( ) = 0.,
d
dt
p
11
t( ) = -5.08 p
10
t( ) - 62.46 p
11
t( ) + 63.51 p
12
t(),
d
dt
p
12
t( ) = -5.08 p
11
t( ) - 68.59 p
12
t( ) + 69.64 p
13
t(),
d
dt
p
13
t( ) = -5.08 p
12
t( ) - 74.72 p
13
t( ) + 75.77 p
14
t(),
p
0
0( ) = 1.0,
d
dt
p
0
t( ) = -5.08 p
0
t( ) + 4.12 p
1
t(),
d
dt
p
1
t( ) = 5.08 p
0
t( ) - 9.20 p
1
t( ) + 8.24 p
2
t(),
d
dt
p
2
t( ) = 5.08 p
1
t( ) - 13.32 p
2
t( ) + 12.36 p
3
t(),
d
dt
p
3
t( ) = 5.08 p
2
t( ) - 17.44 p
3
t( ) + 16.48 p
4
t(),
d
dt
p
14
t( ) = -5.08 p
13
t( ) - 80.85 p
14
t( ) + 81.90 p
15
t(),
d
dt
p
15
t( ) = -5.08 p
14
t( ) - 86.98 p
15
t( ) + 88.03 p
16
t(),
d
dt
p
4
t( ) = 5.08 p
3
t( ) - 21.56 p
4
t( ) + 20.60 p
5
t(),
d
dt
p
5
t( ) = -5.08 p
4
t( ) - 25.68 p
5
t( ) + 26.73 p
6
t(),
d
dt
p
6
t( ) = -5.08 p
5
t( ) - 31.81 p
6
t( ) + 32.86 p
7
t()
?
?
?
> Runge_Kutt:=dsolve(ODESystemInit, numeric,
method=rkf45, {seq(p[i](t), i=0..n+s+1)});
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., p
16
t( ) = 0.]
> add(rhs(Lpi[0][i]), i=2..18);
1.
> Lpi[1]:=Runge_Kutt(0.5);
Lpi
1
:= [t = 0.5, p
0
t( ) = 0.340401647897382365, p
1
t( ) = 0.364677900173566716,
p
2
t( ) = 0.193221444902965223, p
3
t( ) = 0.0653159171913234166, p
4
t( ) = 0.0132105931838467413,
p
5
t( ) = -0.00138277388120118528, p
6
t( ) = 0.00123882561463393450,
d ? d p (t)? - ? d p (t)? - ? d p (t)? - ? d p (t)? - ? d p (t)? - ? d p (t)?
-?
? p2(t)?
? -? 3 ? ? 4 ? ? 5 ? ? 6 ? ? 7 ? ? 8 ?
? dt ? ? dt ? ? dt ? ? dt ? ? dt ? ? dt ? ? dt ?
d ? d p (t)? - ? d p (t)? - ? d p (t)? - ? d p (t)? - ? d p (t)?
-?
? p9(t)?
? -? 10 ? ? 11 ? ? 12 ? ? 13 ? ? 14 ?
? dt ? ? dt ? ? dt ? ? dt ? ? dt ? ? dt ?
d
-?
? p15(t)?
? , p1(0) = 0., p2(0) = 0., p3(0) = 0., p4(0) = 0.,
? dt ?
d d
p8(t) = -5.08 p7(t) - 44.07 p8(t) + 45.12 p9(t), p (t) = -5.08 p8(t) - 50.20 p9(t) + 51.25 p10(t),
dt dt 9
p5(0) = 0., p6(0) = 0., p7(0) = 0., p8(0) = 0., p9(0) = 0.,
d
p (t) = -5.08 p9(t) - 56.33 p10(t) + 57.38 p11(t), p10(0) = 0., p11(0) = 0., p12(0) = 0., p13(0) = 0.,
dt 10
d
p14(0) = 0., p15(0) = 0., p16(0) = 0., p (t) = -5.08 p10(t) - 62.46 p11(t) + 63.51 p12(t),
dt 11
d d
p12(t) = -5.08 p11(t) - 68.59 p12(t) + 69.64 p13(t), p (t) = -5.08 p12(t) - 74.72 p13(t) + 75.77 p14(t),
dt dt 13
d d
p0(0) = 1.0, p0(t) = -5.08 p0(t) + 4.12 p1(t), p (t) = 5.08 p0(t) - 9.20 p1(t) + 8.24 p2(t),
dt dt 1
d d
p2(t) = 5.08 p1(t) - 13.32 p2(t) + 12.36 p3(t), p (t) = 5.08 p2(t) - 17.44 p3(t) + 16.48 p4(t),
dt dt 3
d d
p14(t) = -5.08 p13(t) - 80.85 p14(t) + 81.90 p15(t), p (t) = -5.08 p14(t) - 86.98 p15(t) + 88.03 p16(t),
dt dt 15
d d
p4(t) = 5.08 p3(t) - 21.56 p4(t) + 20.60 p5(t), p (t) = -5.08 p4(t) - 25.68 p5(t) + 26.73 p6(t),
dt dt 5
d ?
p6(t) = -5.08 p5(t) - 31.81 p6(t) + 32.86 p7(t)?
dt ?
> Runge_Kutt:=dsolve(ODESystemInit, numeric,
method=rkf45, {seq(p[i](t), i=0..n+s+1)});
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., p16(t) = 0.]
> add(rhs(Lpi[0][i]), i=2..18);
1.
> Lpi[1]:=Runge_Kutt(0.5);
Lpi1 := [t = 0.5, p0(t) = 0.340401647897382365, p1(t) = 0.364677900173566716,
p2(t) = 0.193221444902965223, p3(t) = 0.0653159171913234166, p4(t) = 0.0132105931838467413,
p5(t) = -0.00138277388120118528, p6(t) = 0.00123882561463393450,
215
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