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GATE 2026 MA – Question 30

Numerical Analysis · Numerical Initial Value Problems · 1 mark · Numerical answer

For y′ = x+y, y(0) = 1, use modified Euler with h = 0.05. Find the second approximation to y(h) to two decimals.

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Correct answer: 1.00 to 1.10

Explanation

Euler predictor gives y_p = 1+0.05×1 = 1.05. The trapezoidal corrector gives y_c = 1+(0.05/2)[1+(0.05+1.05)] = 1.0525, rounding to **1.05**. A second corrector gives 1.0525625 and the same rounded value.

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