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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

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Persamaan Tak Linear (Kaedah Terbuka)

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  1. 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

  2. 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

  3. Kaedah Lelaran Titik Tetap • Kaedah yang paling mudah • pengubahsuaian persamaan asal f(x) = 0 menjadi: • seterusnya proses lelaran dimulakan dengan suatu nilai awal

  4. 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

  5. Kaedah Newton-Raphson • Kaedah ini, jika ia menumpu, kadar penumpuannya berlaku dengan cepat. f(x0) f(x1) r x1 x0

  6. Formula Newton-Raphson • Dari rajah, • Secara am:

  7. 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

  8. ContohKaedah Newton-Raphson • Anggarkan punca bagi: • Ambil nilai awal • Formula: • Contoh

  9. 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.

  10. f(xi) f(xi-1) • kecerunan garis yang menghubungkan titik xi dan xi-1 adalah: • maka xi-1 r xi+1 xi

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

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