Home › Previous year questions › GATE 2017 CE (CE1) › Question 47GATE 2017 CE (CE1) – Question 47 Engineering Mathematics · Numerical Methods: Error analysis, algebraic equations, interpolation, differentiation, integration, ODEs · 2 marks · Numerical answer
Solve $du/dt=3t^2+1$, with $u(0)=0$, numerically using forward Euler with step $\Delta t=2$. Find the absolute error at the end of the first step.
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Show answer and explanation Correct answer: 7.95 to 8.05
Explanation Forward Euler uses the slope at the start: $u_1=u_0+\Delta t(3t_0^2+1)=0+2(1)=2$. The exact integral is $u(t)=t^3+t$, so $u(2)=8+2=10$. The absolute error is $|10-2|=8$. A slope evaluated at the end of the interval would be a different integration method.
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