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Persamaan Tak Linear (Kaedah Terbuka)

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persamaan tak linear kaedah terbuka
This presentation will probably involve audience discussion, which will create action items. Use PowerPoint to keep track of these action items during your presentation
  • In Slide Show, click on the right mouse button
  • Select “Meeting Minder”
  • Select the “Action Items” tab
  • Type in action items as they come up
  • Click OK to dismiss this box
  • This will automatically create an Action Item slide at the end of your presentation with your points entered.

Persamaan Tak Linear(Kaedah Terbuka)

Bahari Idrus

Jabatan Komputeran Industri

FTSM

kaedah terbuka
Kaedah Terbuka
  • kaedah yang mengesan punca secara lelaran dengan menggunakan satu atau dua titik permulaan.
  • Kaedah-Kaedah yang di bincangkan:
    • Kaedah lelaran tepat
    • kaedah Newton-Raphson
    • Kaedah Sekan
kaedah lelaran titik tetap
Kaedah Lelaran Titik Tetap
  • Kaedah yang paling mudah
  • pengubahsuaian persamaan asal f(x) = 0 menjadi:
  • seterusnya proses lelaran dimulakan dengan suatu nilai awal
contoh
Contoh
  • Dapatkan punca bagi e-x-x tepat kepada 3 angka perpuluhan. Nilai awal x0 = 0
  • Penyelesaian:

f(x) = e-x-x =0

x = e-x

Maka, formula lelaran:

xi+1=e-xi

  • Contoh
kaedah newton raphson
Kaedah Newton-Raphson
  • Kaedah ini, jika ia menumpu, kadar penumpuannya berlaku dengan cepat.

f(x0)

f(x1)

r

x1

x0

formula newton raphson
Formula Newton-Raphson
  • Dari rajah,
  • Secara am:
algoritma kaedah newton raphson
Algoritma Kaedah Newton-Raphson
  • Mula
  • pilih nilai awal x0 dan 
  • kira f(xi) dan f’(xi). Jika f’(xi)0, ulangi langkah 1 untuk nilai awal yg lain.
  • Jika |f(xi)/f’(xi)|, xi ialah penyelesaian. Jika tidak terus ke langkah 4.
  • kirakan xi+1=xi-f(xi)/f’(xi) dengan i=0,1,2,...
  • Gantikan xi dengan xi+1 dan ulangi langkah 2 untuk xi terkini
  • tamat
contoh kaedah newton raphson
ContohKaedah Newton-Raphson
  • Anggarkan punca bagi:
  • Ambil nilai awal
  • Formula:
  • Contoh
kaedah sekan
Kaedah Sekan
  • Kaedah Sekan digunakan untuk menggelakkan penggunaan terbitan yang ada pada kaedah Newton-Raphson.
  • Ini disebabkan, terdapat terbitan yang sukar diperolehi.
  • Terbitan boleh diperolehi melalui beza terbahagi terhingga.
slide10
f(xi)

f(xi-1)

  • kecerunan garis yang menghubungkan titik xi dan xi-1 adalah:
  • maka

xi-1

r

xi+1

xi

contoh1
Contoh
  • dapatkan punca
  • dengan nilai awal x-1=0 dan x0=1.0
  • Contoh
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