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GATE 2018 ME (ME1) – Question 47

Engineering Mathematics · Numerical Methods: Algebraic equations, integration by trapezoidal and Simpson rules, ODE methods · 2 marks · Numerical answer

Use explicit forward Euler on $dy/dt=y$ with step 0.1 and y(0) = 1. The computed y(1), to two decimals, is ______.

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Correct answer: 2.55 to 2.65

Explanation

Euler update is $y_{n+1}=y_n+0.1y_n=1.1y_n$. Ten steps reach t = 1, giving $y_{10}=1.1^{10}=2.593742$, rounded to 2.59.