GATE 2024 MA – Question 22

Numerical Analysis · Numerical Initial Value Problems · 1 mark · Multiple choice

For y′=f(x,y), use y_n=y_(n−1)+ak₁+bk₂, with k₁=hf(x_(n−1),y_(n−1)), k₂=hf(x_(n−1)+αh,y_(n−1)+βk₁). Which (a,b,α,β) gives order two?

(1,1,0.5,0.5)
(0.5,0.5,2,2)
(0.25,0.75,2/3,2/3)
(0.5,0.5,1,2)

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Show answer and explanation

Correct answer: (C) (0.25,0.75,2/3,2/3)

Explanation

Matching Taylor terms through h² requires a+b=1, bα=1/2 and bβ=1/2. Only C has 0.25+0.75=1 and 0.75×(2/3)=1/2 for both coefficients. **C**.

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