Bisection Method

<aside> 1️⃣ Check if the root is exist

$$ f(x_l)*f(x_u) > 0 $$

If Result > 0 ⇒ Stop ⇒ ‘The Root is not exist’ else Continue

</aside>

<aside> 2️⃣ Calculate xr

$$ x_r=\frac{x_l+ x_u}{2} $$

</aside>

<aside> 3️⃣ Calculate f(xr)

</aside>

<aside> 4️⃣ Check a Sign of f(xr) with f(xu)

• If both are +ve or -ve ⇒ Result is +ve

• If one is -ve and the other is +ve ⇒ Result is -ve

  If Result is -ve

  xl = xr , f(xl) = f(xr)

  If Result is +ve

  xu = xr , f(xu) = f(xr)

</aside>

<aside> 5️⃣ Calculate Ea

$$ \varepsilon_a=\left| \frac{x_r-x_r\text{old}}{x_r} \right|*100 $$

</aside>

Go to Step 2 :)

False Position Method

<aside> 1️⃣ Check if the root is exist

$$ f(x_l)*f(x_u) > 0 $$

If Result > 0 ⇒ Stop ⇒ ‘The Root is not exist’ else Continue

</aside>

<aside> 2️⃣ Calculate xr

$$ x_r=x_u-\frac{f(x_u)*(x_l-x_u)}{f(x_{l})-f(x_u)} $$

</aside>

<aside> 3️⃣ Calculate f(xr)

</aside>

<aside> 4️⃣ Check a Sign of f(xr) with f(xu)

• If both are +ve or -ve ⇒ Result is +ve

• If one is -ve and the other is +ve ⇒ Result is -ve

  If Result is -ve

  xl = xr , f(xl) = f(xr)

  If Result is +ve

  xu = xr , f(xu) = f(xr)

</aside>

<aside> 5️⃣ Calculate Ea

$$ \varepsilon_a=\left| \frac{x_r-x_r\text{old}}{x_r} \right|*100 $$

</aside>

Go to Step 2 :)