GATE 2021 MA – Question 18

Numerical Analysis · Nonlinear Equations · 1 mark · Multiple choice

For x_(n+1)=φ(x_n),φ(x)=3+(x−3)³ on (2.5,3.5), and x₀=3.25, find the convergence order.

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Correct answer: (C) 3

Explanation

The fixed point is 3. Its error satisfies exactly e_(n+1)=e_n³, with e₀=1/4 ensuring convergence. The limiting ratio |e_(n+1)|/|e_n|³=1, so order **3, C**.

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