GATE 2021 MA – Question 41

Numerical Analysis · Numerical Initial Value Problems · 2 marks · Multiple choice

Explicit Euler solves y′=−10y,t>0,y(0)=1 via y_(n+1)=y_n+h f(t_n,y_n). Which step range ensures y_n→0?

Show answer and explanation

Correct answer: (A) 0<h<0.2

Explanation

The iterates are y_n=(1−10h)ⁿ. Decay requires |1−10h|<1, equivalent to 0<h<0.2. Thus **A**.

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