david - lembar jawaban uts metnum - 2010

7/26/2019 David - Lembar Jawaban UTS Metnum - 2010

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Lembar Jawaban UTS Metode Numerik

David Silalahi

1507165730

S1 Teknik imia Non!e" #015

1$ Selesaikan sistem persamaan linier berikut,

menggunakan Metode Invers Matrik

Penyelesaian:Analisa Data

Jumlah Persamaan : 4

Jumlah Variable : 4

DoF : dapat diselesaikan dengan Metode Matrik Invers

Persamaan !inier Dikonversikan "e

Persamaan Matrik # A X$ b %

X$ A&'

bData diinput ke Program ()*el

Sehingga diperoleh data sebagai berikut

Dan nilai X adalah

X

X1 = 1

X2 = #

X3 = 3

X4 = %

#$ Selesaikan sistem persamaan di+erensial

berikut dengan metode (uler:

"ondisi aalY'$Y-$ ' pada X$

a. Selesaikan sistem persamaan di+erensial di

atas dengan metode (uler hingga X$ ' /X$ ,'0

b. PlotY',Y-terhadap X/lengkapi gra+ik denganlegend dan title0

Penyelesaian:1entuk 1aku Metode (uler

a. Data

Y', $Y-, $ '

Persamaann untuk menghitung nilai

Tabel Perhitunganj x y1&j + 1 y#&j + 10 ' '

1 ,'1,1010050

20,9494974

9

2 ,-1,2066919

50,8976900

7

3 ,2 1,31628670,8449994

8

4 ,41,4288852

50,7918842

5

5 ,31,5434814

80,7388241

6

6 , 1,65900260,6863026

6

7 ,51,7743497

90,6347885

7

8 ,6 1,88844080,5847186

8

9 ,72,0002509

10,5364823

5

10 ,'2,1088492

80,4904096

2

11 ,''2,2134276

20,4467632

9

12 ,'-2,3133199

60,4057353

613 ,'2 2,4080125 0,3674476


2/4

4 7

14 ,'42,4971445

8 0,3319561

15 ,'32,5805010

80,2992574

6

16 ,'2,6579994

70,2692982

6

17 ,'52,7296722

10,2419842

1

18 ,'62,7956471

70,2171899

8

19 ,'72,8561276

90,1947682

3

20 ,-2,9113733

40,1745577

9

21 ,-'2,9616825

70,1563905

7

22 ,--3,0073776

5 0,1400972

23 ,-23,0487920

40,1255114

6

24 ,-43,0862604

10,1124734

3

25 ,-33,1201108

70,1008318

4

26 ,-3,1506593

20,0904453

6

27 ,-53,1782055

60,0811834

7

28 ,-63,2030307

80,0729266

1

29 ,-7

3,2253962

4 0,0655661

30 ,23,2455427

90,0590037

3

31 ,2'3,2636910

80,0531511

8

32 ,2-3,2800421

30,0479293

4

33 ,223,2947783

7 0,0432676

34 ,243,3080647

20,0391030

8

35 ,233,3200498

7

0,0353799

2

36 ,23,3308675

40,0320485

5

37 ,253,3406378

10,0290650

7

38 ,263,3494683

4 0,0263906

39 ,273,3574555

30,0239907

5

40 ,43,3646856

40,0218351

1

41 ,4' 3,37123584 0,01989679

42 ,4-3,3771751

10,0181519

9

43 ,423,3825651

20,0165796

8

44 ,443,3874610

10,0151612

4

45 ,433,3919120

50,0138801

9

46 ,43,3959623

40,0127219

4

47 ,453,3996513

10,0116735

3

48 ,46

3,4030142

6 0,0107235

49 ,473,4060828

10,0098616

6

50 ,33,4088852

80,0090789

6

51 ,3'3,4114470

70,0083673

6

52 ,3-3,4137909

60,0077196

8

53 ,323,4159374

20,0071295

5

54 ,343,4179048

20,0065912

9

55 ,333,4197096

90,0060998

1

56 ,3 3,42136690,0056505

9

57 ,353,4228898

70,0052395

6

58 ,363,4242906

50,0048630

9

59 ,373,4255801

40,0045179

4

60 ,3,4267681

70,0042011

8

61 ,'3,4278636

4 0,0039102

62 ,-3,4288745

80,0036426

4

63 ,23,4298082

60,0033963

7

64 ,43,4306712

7 0,0031695

65 ,33,4314695

80,0029603

1

66 ,3,4322086

20,0027672

4

67 ,53,4328933

10,0025888

8

68 ,63,4335281

20,0024239

8

69 ,73,4341171

20,0022713

9

70 ,53,4346640

10,0021300

7

71 ,5'

3,4351721

8

0,0019990

7

72 ,5- 3,43564470,0018775

4

73 ,523,4360843

80,0017647

174 ,54 3,4364937 0,0016598


3/4

7 7

75 ,533,4368752

40,0015623

7

76 ,53,4372309

10,0014716

4

77 ,553,4375627

60,0013871

3

78 ,563,4378725

80,0013083

7

79 ,573,4381620

2 0,0012349

80 ,63,4384325

90,0011663

3

81 ,6'3,4386856

80,0011022

8

82 ,6-3,4389225

60,0010424

1

83 ,623,4391444

1 0,0009864

84 ,64 3,43935230,0009339

8

85 ,633,4395472

30,0008848

8

86 ,63,4397301

10,0008388

6

87 ,653,4399017

8 0,0007957

88 ,663,4400630

30,0007551

9

89 ,673,4402145

60,0007171

5

90 ,7

3,4403570

5

0,0006814

1

91 ,7' 3,44049110,0006478

1

92 ,7-3,4406172

80,0006161

9

93 ,723,4407361

30,0005864

3

94 ,743,4408481

10,0005583

9

95 ,733,4409536

80,0005319

8

96 ,73,4410532

7

0,0005070

6

97 ,753,4411472

50,0004835

6

98 ,763,4412359

80,0004613

7

99 ,773,4413198

10,0004404

1100 1 3,441399 0,000421

b. Plot Y',Y- terhadap X dengan gra+ik dapat

dilihat pada gra+ik berikut :

3$ 8entukan spesi+ik volume ammonia dengan

metode neton

P $ Pressure /' atm09 8 $ 8emperature

/-3o

"09 V $ Spe*i+i* Volume /litergmole09 ;$ .6- /liter&atmgmol&"0. Van der


4/4

2 ,-653 0,0402

4 ,2-3 0,0634

3 ,26'-3 0,0933

,4253 0,1302

5 ,47253 0,1749

6 ,33 0,2277

7 ,-3 0,2892

' ,-3 0,3598'' ,5'653 0,44

'- ,553 0,5302

'2 ,62'-3 0,6309

'4 ,6653 0,7425

'3 ,74253 0,8654

' ' 1

Trapezoidal

0''1((067

Simpsons

0'75636%'

5$ sing +olloing table to obtain an

interpolated value +or @ at +olloing values o+) $ '2, B $ ' -2 bB *ubi* interpolation

Penyelesaian:

8ranspose 8abel ntuk Memperoleh nilai CPada $', E $' '2, serta $ - E $' '2

y )

1,6 #%'(7 ! "a#a $aat y=1%6 #an

x=1 1&3'

2 1&16(16 ! "a#a $aat y=2 #an

x=1 1&3'

Perhitungan >ilai B) pada saat ) $ ' -2

Di*eroleh nilai +, - #&03301

david - lembar jawaban uts metnum - 2010

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