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Самарский национальный исследовательский университет им. ак. С.П. Королёва (бывш. СГАУ, СамГУ)

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[НЕСОРТИРОВАННОЕ]

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Vychislitelny_praktikum

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β5Mk =	b5M k =	m
0.029948	0.029851	m			k
		∑	b5Mk	(−1)		= 1
-0.094859	-0.094664	∑	b5Mk	(−1)		= 1
		k = 0
0.210559	0.210267	k = 0
0.210559	0.210267

-0.350974	-0.350585

0.434154	0.433667

-0.353464	-0.35288

0.071981	0.071299

0.274272	0.275051

-0.41309	-0.413966

0.189251	0.190224

0.186837	0.185766

-0.292016	-0.290847

0.022924	0.021658

0.21321	0.214573

-0.084344	-0.085804

-0.139691	-0.138134

	0.6
	0.36
β5M k	0.12
b5M k
− 0.12
− 0.36
	− 0.60	3	6	9	12	15
				k

2. Построить графические зависимости δ от параметра χ; μ = 0 - 5, m = 2 - 6. Определить количество локальных экстремумов, значения параметра χopt и соотвествующие им значения погрешностей.

τ4 (ω) := 2 λ(2 + ω2 ) 4 λ λ2 + ω2

χ := γ

233

	⌠	∞	− λ τ
β5(k ,χ ,ω) := 2χ (k + 1)		P7(k ,τ ,χ) e	− λ τ	cos (ω τ ) dτ

	⌡
	0

		k			m		s
	2 (−1)	k	(k + 1)		− ∑		s
	2 (−1)		(k + 1)	1	− ∑	(−1)		β5(s ,χ ,ω)
b5(k ,χ ,ω) := β5(k ,χ ,ω) +					s = 0
b5(k ,χ ,ω) := β5(k ,χ ,ω) +			(m		+ 1) (m + 2)
			(m		+ 1) (m + 2)

	1		m		(b5(k ,χ ,ω))2
δ1(χ ,m,ω) :=	1 −		∑
δ1(χ ,m,ω) :=	1 −	2 χ τ4 (ω)	∑		k + 1
			k = 0
i := 0 .. 100
δ2V0i := δ1(i 0.1 + 0.01,2,0)				δ2V2i := δ1(i 0.1 + 0.01,2,2)		δ2V4i := δ1(i 0.1 + 0.01,2,4)
δ2V1i := δ1(i 0.1 + 0.01,2,1)				δ2V3i := δ1(i 0.1 + 0.01,2,3)		δ2V5i := δ1(i 0.1 + 0.01,2,5)

δ2M 0		:= δ2V0	δ2M 2 := δ2V2			δ2M 5 := δ2V5
δ2M		:= δ2V1	δ2M	3	:= δ2V3	δ2M	4	:= δ2V4
	1

234

		1
(δ2M 0 )
(δ2M	1 )i0.833
		i
(δ2M	2 )0.667
		i
(δ2M	3 )	0.5
		i
(δ2M	4 )	i0.333
		i0.333
(δ2M	5 )	i0.167
		i0.167
		0	2	4	6	8	10
					i 0.1+0.01


δ3V0i	:= δ1(i 0.1 + 0.01,2,5)		δ3V2i	:= δ1(i 0.1 + 0.01,4,5)		δ3V4i := δ1(i 0.1 + 0.01,6,5)
δ3V1i	:= δ1(i 0.1 + 0.01,3,5)		δ3V3i	:= δ1(i 0.1 + 0.01,5,5)
δ3M 0		:= δ3V0	δ3M 2		:= δ3V2	δ3M 4 := δ3V4
δ3M 1		:= δ3V1	δ3M 3		:= δ3V3

235

							1
(δ3M			0 )		i0.867
					i0.867
(δ3M			1 )		i0.733
(δ3M			2 )		i0.733
(δ3M			2 )		i	0.6
					i
(δ3M 3 )
(δ3M			4 )i0.467
					i
					0.333
						0.2 0									2			4	6	8	10
																			i 0.1+0.01
(			0 )			= 0.52
min δ3M						= 0.52
	(		(				0 )					0 )						3.41
match	(		(	δ3M			0 )			,δ3M		0 )		0.1
match		min		δ3M						,δ3M				0.1		+ 0.01 = 3.51
																		3.61
χminM			:= match					(		(	δ3M		0 )		,	δ3M	0 )	1 0.1	+ 0.01
χminM		0	:= match						min		δ3M				,	δ3M		1 0.1	+ 0.01
		0
(			1 )			= 0.439
min δ3M						= 0.439
match	(		(	δ3M			1 )			,δ3M		1 )		0.1 + 0.01 = ( 1.81)
match		min		δ3M						,δ3M				0.1 + 0.01 = ( 1.81)
χminM			:= match					(		(	δ3M		1 )		,	δ3M	1 )	0 0.1	+ 0.01
χminM		1	:= match						min		δ3M				,	δ3M		0 0.1	+ 0.01
		1
(			2 )			= 0.372
min δ3M						= 0.372
match	(		(	δ3M			2 )			,δ3M		2 )		0.1 + 0.01 = ( 2.21)
match		min		δ3M						,δ3M				0.1 + 0.01 = ( 2.21)
χminM			:= match					(		(	δ3M		2 )		,	δ3M	2 )	0 0.1	+ 0.01
χminM		2	:= match						min		δ3M				,	δ3M		0 0.1	+ 0.01
		2

236

min(δ3M 3 ) = 0.318

match(min(δ3M 3 ),δ3M 3 ) 0.1 + 0.01 = ( 1.41)

χminM3 := match(min(δ3M 3 ),δ3M 3 )0 0.1 + 0.01

min(δ3M 4 ) = 0.276

match(min(δ3M 4 ),δ3M 4 ) 0.1 + 0.01 = ( 1.61)

χminM4 := match(min(δ3M 4 ),δ3M 4 )0 0.1 + 0.01

	3.51

	1.81

χminM = 2.21

1.411.61

j := 0.. 4 min(δ3M j )

0.52

0.439

0.372

0.318

0.276

3. Построить графические зависимости δ от параметра μ, m; μ = 0 - 5, m = 2 - 6, χopt.

ω1 := 0.. 5

δ4V0ω1	:= δ1(χminM0,2,ω1)	δ4V2ω1	:= δ1(χminM2,4,ω1)	δ4V4ω1 := δ1(χ ,6,ω1)
δ4V1ω1	:= δ1(χminM1,3,ω1)	δ4V3ω1	:= δ1(χminM3,5,ω1)

237

δ4M 0 := δ4V0				δ4M 2 := δ4V2			δ4M 4 := δ4V4
δ4M 1 := δ4V1				δ4M 3	:= δ4V3
		0.6
(δ4M 0 )		ω10.5
(δ4M	1 )	ω10.5
		ω2
(δ4M	2 )	0.4
		ω1
(δ4M	3 )	0.3
		ω1
(δ4M	4 )	ω10.2
		ω10.2
(δ4M	5 )	ω10.1
		ω10.1
		0	1	2	3	4	5
				ω1
m2 := 2.. 6
δ5V0m2 := δ1(χminMm2−2,m2,0)				δ5V2m2 := δ1(χminMm2−2,m2,2)			δ5V4m2 := δ1(χminMm2−2,m2,4)
δ5V1m2 := δ1(χminMm2−2,m2,1)				δ5V3m2 := δ1(χminMm2−2,m2,3)			δ5V5m2 := δ1(χminMm2−2,m2,5)
δ5V1m2 := δ1(χminMm2−2,m2,1)

δ5M 0 := δ5V0	δ5M 2 := δ5V2	δ5M 4 := δ5V4
δ5M 1 := δ5V1	δ5M 3 := δ5V3	δ5M 5 := δ5V5

238

	0.6
(δ5M 0 )
(δ5M	1 )m20.5
	m2
(δ5M	2 ) 0.4
	m2
(δ5M	3 ) 0.3
	m2
(δ5M	4 )
	m20.2
(δ5M	5 )
	m20.1
	2	2.8	3.6	4.4	5.2	6
				m2
4. Построить графические зависимости δ от параметра μ, m; μ = 0 - 5, m = 2 - 6, χ1, χ2.

t :=	1		8 0.02
t :=	λ		ω 2	− 1
	λ		ω 2
			λ
			λ
χ1m2 :=		0.4			χ1m2 =		0.4
		(m2 + 1)		t		χ1c(mx) :=	0.4
							(mx + 1) t

					1.633
					1.633

					1.225

					0.98

					0.816

					0.7

δ6V0ω1	:= δ1(χ12,2,ω1)	δ6V2ω1	:= δ1(χ14,4,ω1)	δ6V4ω1 := δ1(χ16,6,ω1)
δ6V1ω1	:= δ1(χ13,3,ω1)	δ6V3ω1	:= δ1(χ15,5,ω1)
δ6M 0 := δ6V0		δ6M 2 := δ6V2		δ6M 4 := δ6V4
δ6M 1	:= δ6V1	δ6M 3 := δ6V3

239

		0.8
(δ6M	0 )	ω10.667
		ω10.667
(δ6M	1 )	ω10.533
(δ6M	2 )	ω10.533
(δ6M	2 )	ω1 0.4
(δ6M 3 )		ω1 0.4
(δ6M 3 )		ω10.267
(δ6M	4 )	ω10.267
		ω1
		0.133
		0	1	2	3	4	5
				ω1
δ7V0m2 := δ1(χ1m2,m2,0)				δ7V2m2 := δ1(χ1m2,m2,2)			δ7V4m2 := δ1(χ1m2,m2,4)
δ7V1m2 := δ1(χ1m2,m2,1)				δ7V3m2 := δ1(χ1m2,m2,3)			δ7V5m2 := δ1(χ1m2,m2,5)
δ7V1m2 := δ1(χ1m2,m2,1)				δ7V3m2 := δ1(χ1m2,m2,3)
δ7M 0 := δ7V0				δ7M 2 := δ7V2			δ7M 4 := δ7V4
δ7M 1		:= δ7V1		δ7M 3	:= δ7V3		δ7M 5 := δ7V5

240

		0.8
(δ7M 0 )
(δ7M	1 )m20.667
	m2
(δ7M	2 ) 0.533
	m2
(δ7M	3 )	0.4
	m2
(δ7M	4 )
	m20.267
(δ7M	5 )
	m20.133
		2			2.8	3.6	4.4	5.2	6
						m2
λ2 + ω2
χ2m2 := (m2 + 1)			χ2	m2	=		χ2c(mx) :=	λ2 + ω2
				m2	1.7		χ2c(mx) :=	(mx + 1)
					1.7
				1.275
				1.02
				0.85
				0.728
δ8V0ω1 := δ1(χ22,2,ω1)						δ8V2ω1 := δ1(χ24,4,ω1)		δ8V4ω1 := δ1(χ26,6,ω1)
δ8V1ω1 := δ1(χ23,3,ω1)						δ8V3ω1 := δ1(χ25,5,ω1)
δ8M 0 := δ8V0						δ8M 2 := δ8V2		δ8M 4	:= δ8V4
δ8M 1 := δ8V1						δ8M 3 := δ8V3
									241

		0.8
(δ8M	0 )	ω10.667
		ω10.667
(δ8M	1 )	ω10.533
(δ8M	2 )	ω10.533
(δ8M	2 )	ω1 0.4
(δ8M 3 )		ω1 0.4
(δ8M 3 )		ω10.267
(δ8M	4 )	ω10.267
		ω1
		0.133
		0	1	2	3	4	5
				ω1
δ9V0m2 := δ1(χ2m2,m2,0)				δ9V2m2 := δ1(χ2m2,m2,2)			δ9V4m2 := δ1(χ2m2,m2,4)
δ9V1m2 := δ1(χ2m2,m2,1)				δ9V3m2 := δ1(χ2m2,m2,3)			δ9V5m2 := δ1(χ2m2,m2,5)
δ9V1m2 := δ1(χ2m2,m2,1)				δ9V3m2 := δ1(χ2m2,m2,3)
δ9M 0 := δ9V0				δ9M 2 := δ9V2			δ9M 4 := δ9V4
δ9M 1		:= δ9V1		δ9M 3	:= δ9V3		δ9M 5 := δ9V5
		0.8

(δ9M 0 )
	1 )m20.667

(δ9M
		m2
(δ9M	2 ) 0.533
(δ9M	2 ) 0.533
		m2
(δ9M	3 )	0.4
(δ9M	3 )	0.4
		m2
(δ9M	4 )
(δ9M	4 )	m20.267
		m20.267
(δ9M	5 )	m20.133

2.8

3.6

4.4

5.2

242

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