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Mata Kuliah : Metode Numerik�Minggu ke 3

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Mahasiswa dapat melakukan komputasi dalam menemukan akar suatu persamaan dengan pendekatan Bisection

Tujuan perkuliahan

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Bisection’s Basic

Theorem

An equation f(x)=0, where f(x) is a real continuous function, has at least one root between xl and xu if f(xl) f(xu) < 0.

Figure 1 At least one root exists between the two points if the function is real, continuous, and changes sign.

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Bisection’s Basic

 

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Algorithm

  •  

1 Iteration

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Error’s Calculation

  •  

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Example

  • Finding roots of

 

With maximal three iteration or relative error of 5%

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  •  

Example

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​

​

​

​

​

​

error

0

0,11

0,0003993

-0,0002662

0,055

0,00006655

​

0,055

0,11

0,00006655

-0,0002662

0,0825

-0,000162216

0,333333

0,055

0,0825

0,00006655

-0,000162216

0,06875

-5,56316E-05

0,2

0,055

0,06875

0,00006655

-5,56316E-05

0,061875

4,48433E-06

0,111111

0,06188

0,06875

4,48433E-06

-5,56316E-05

0,065313

-2,59392E-05

0,052632

0,06188

0,06531

4,48433E-06

-2,59392E-05

0,063594

-1,08036E-05

0,027027

0,06188

0,06359

4,48433E-06

-1,08036E-05

0,062734

-3,17678E-06

0,013699

0,06188

0,06273

4,48433E-06

-3,17678E-06

0,062305

6,49728E-07

0,006897

Example

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