1406574812_nadifa ismaningtyas

8/17/2019 1406574812_Nadifa Ismaningtyas

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PEMODELAN TEKNIK KIMIA

METODE EULER DAN ADAM-BASHFORD

Nadifa Ismaningtyas (1406574812)

PROGRAM STUDI TEKNIK KIMIA

FAKULTAS TEKNIK UNIVERSITAS INDONESIA

DEPOK, MEI 2016



I.

Metode Euler

Persamaan untuk metode Euler:

Soal:

a. List Program

b.

Hasil Pemrograman

10

y

yt dt

dy



c. Pembuktian dengan Excel

i tn yn f(yn) h.f(yn)

0 0.0 1 1 0.1

1 0.1 1.1 1.2 0.12

2 0.2 1.22 1.42 0.142

3 0.3 1.362 1.662 0.1662

4 0.4 1.5282 1.9282 0.192825 0.5 1.72102 2.22102 0.222102



6 0.6 1.943122 2.543122 0.254312

7 0.7 2.197434 2.897434 0.289743

8 0.8 2.487178 3.287178 0.328718

9 0.9 2.815895 3.715895 0.37159

10 1.0 3.187485 4.187485 0.418748

11 1.1 3.606233 4.706233 0.470623

12 1.2 4.076857 5.276857 0.527686

13 1.3 4.604542 5.904542 0.590454

14 1.4 5.194997 6.594997 0.6595

15 1.5 5.854496 7.354496 0.73545

16 1.6 6.589946 8.189946 0.818995

17 1.7 7.408941 9.108941 0.910894

18 1.8 8.319835 10.11983 1.011983

19 1.9 9.331818 11.23182 1.123182

20 2.0 10.455 12.455 1.245521 2.1 11.7005 13.8005 1.38005

22 2.2 13.08055 15.28055 1.528055

23 2.3 14.6086 16.9086 1.69086

24 2.4 16.29947 18.69947 1.869947

25 2.5 18.16941 20.66941 2.066941

26 2.6 20.23635 22.83635 2.283635

27 2.7 22.51999 25.21999 2.521999

28 2.8 25.04199 27.84199 2.784199

29 2.9 27.82619 30.72619 3.072619

30 3.0 30.8988 33.8988 3.38988

31 3.1 34.28868 37.38868 3.738868

32 3.2 38.02755 41.22755 4.122755

33 3.3 42.15031 45.45031 4.545031

34 3.4 46.69534 50.09534 5.009534

35 3.5 51.70487 55.20487 5.520487

36 3.6 57.22536 60.82536 6.082536

37 3.7 63.3079 67.0079 6.70079

38 3.8 70.00869 73.80869 7.380869

39 3.9 77.38956 81.28956 8.12895640 4.0 85.51851 89.51851 8.951851

II. Metode Adam-Bashford Orde 2

Persamaan untuk metode Adam-Bashford Orde 2:



Untuk suku pertama dihitung menggunakan metode Euler, karena metode Adam-

Bashford Orde 2 membutuhkan nilai −1 dan , sehingga baru bisa dimulai untuk

menghitung suku kedua.

Soal:

a. List Program

b.

Hasil Pemrograman

10

y

yt dt

dy




i tn yn-1 f(yn-1) yn f(yn)

0 0.0 - - 1 1

1 0.1 1 1.0 1.1 1.2

2 0.2 1.1 1.2 1.23 1.43

3 0.3 1.23 1.43 1.3845 1.6845

4 0.4 1.3845 1.6845 1.565675 1.965675

5 0.5 1.565675 1.965675 1.776301 2.276301

6 0.6 1.776301 2.276301 2.019463 2.619463

7 0.7 2.019463 2.619463 2.298567 2.998567

8 0.8 2.298567 2.998567 2.617379 3.417379

9 0.9 2.617379 3.417379 2.980057 3.880057



10 1.0 2.980057 3.880057 3.391197 4.391197

11 1.1 3.391197 4.391197 3.855874 4.955874

12 1.2 3.855874 4.955874 4.379695 5.579695

13 1.3 4.379695 5.579695 4.968856 6.268856

14 1.4 4.968856 6.268856 5.630199 7.030199

15 1.5 5.630199 7.030199 6.371286 7.871286

16 1.6 6.371286 7.871286 7.200469 8.800469

17 1.7 7.200469 8.800469 8.126975 9.826975

18 1.8 8.126975 9.826975 9.160998 10.961

19 1.9 9.160998 10.961 10.3138 12.2138

20 2.0 10.3138 12.2138 11.59782 13.59782

21 2.1 11.59782 13.59782 13.0268 15.1268

22 2.2 13.0268 15.1268 14.61593 16.81593

23 2.3 14.61593 16.81593 16.38198 18.68198

24 2.4 16.38198 18.68198 18.34348 20.7434825 2.5 18.34348 20.74348 20.5209 23.0209

26 2.6 20.5209 23.0209 22.93687 25.53687

27 2.7 22.93687 25.53687 25.61635 28.31635

28 2.8 25.61635 28.31635 28.58696 31.38696

29 2.9 28.58696 31.38696 31.87919 34.77919

30 3.0 31.87919 34.77919 35.52672 38.52672

31 3.1 35.52672 38.52672 39.56677 42.66677

32 3.2 39.56677 42.66677 44.04044 47.24044

33 3.3 44.04044 47.24044 48.99317 52.29317

34 3.4 48.99317 52.29317 54.47513 57.87513

35 3.5 54.47513 57.87513 60.54174 64.04174

36 3.6 60.54174 64.04174 67.25424 70.85424

37 3.7 67.25424 70.85424 74.68029 78.38029

38 3.8 74.68029 78.38029 82.89462 86.69462

39 3.9 82.89462 86.69462 91.9798 95.8798

40 4.0 91.9798 95.8798 102.027 106.027

III. Metode Adam-Bashford Orde 4

Persamaan untuk metode Adam-Bashford Orde 4:

Untuk suku pertama, kedua, dan ketiga dihitung menggunakan metode Euler, karena

metode Adam-Bashford Orde 4 membutuhkan nilai −3, −2, −1, dan ,

sehingga baru bisa dimulai untuk menghitung suku keempat.

Soal:



a. List Program

b.

Hasil Pemrograman

10

y

yt dt

dy




i tn yn-1 f(yn-1) yn f(yn)

0 0.0 - - 1 1

1 0.1 1 1 1.1 1.2

2 0.2 1.1 1.2 1.22 1.4

3 0.3 1.22 1.42 1.362 1.662

4 0.4 1.362 1.662 1.541292 1.941292

5 0.5 1.541292 1.941292 1.751513 2.251513

6 0.6 1.751513 2.251513 1.993225 2.593225

7 0.7 1.993225 2.593225 2.270966 2.970966

8 0.8 2.270966 2.970966 2.588622 3.3886229 0.9 2.588622 3.388622 2.950175 3.850175



10 1.0 2.950175 3.850175 3.360249 4.360249

11 1.1 3.360249 4.360249 3.823973 4.923973

12 1.2 3.823973 4.923973 4.346984 5.546984

13 1.3 4.346984 5.546984 4.935514 6.235514

14 1.4 4.935514 6.235514 5.596456 6.996456

15 1.5 5.596456 6.996456 6.337424 7.837424

16 1.6 6.337424 7.837424 7.166835 8.766835

17 1.7 7.166835 8.766835 8.09399 9.79399

18 1.8 8.09399 9.79399 9.129168 10.92917

19 1.9 9.129168 10.92917 10.28373 12.18373

20 2.0 10.28373 12.18373 11.57023 13.57023

21 2.1 11.57023 13.57023 13.00255 15.10255

22 2.2 13.00255 15.10255 14.59601 16.79601

23 2.3 14.59601 16.79601 16.36758 18.66758

24 2.4 16.36758 18.66758 18.33597 20.7359725 2.5 18.33597 20.73597 20.52189 23.02189

26 2.6 20.52189 23.02189 22.94822 25.54822

27 2.7 22.94822 25.54822 25.64023 28.34023

28 2.8 25.64023 28.34023 28.62587 31.42587

29 2.9 28.62587 31.42587 31.93602 34.83602

30 3.0 31.93602 34.83602 35.60481 38.60481

31 3.1 35.60481 38.60481 39.66996 42.76996

32 3.2 39.66996 42.76996 44.17314 47.37314

33 3.3 44.17314 47.37314 49.16043 52.46043

34 3.4 49.16043 52.46043 54.68273 58.08273

35 3.5 54.68273 58.08273 60.79632 64.29632

36 3.6 60.79632 64.29632 67.56338 71.16338

37 3.7 67.56338 71.16338 75.05263 78.75263

38 3.8 75.05263 78.75263 83.34003 87.14003

39 3.9 83.34003 87.14003 92.5095 96.4095

40 4.0 92.5095 96.4095 102.6538 106.6538

1406574812_nadifa ismaningtyas

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