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GATE ME 2024 Set 1 — Question 11

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MCQ+1 / -0.33MediumSingle & Multi-Step ODE MethodsNumerical MethodsEngineering Mathematics

Engineering Mathematics → Numerical Methods → Single & Multi-Step ODE Methods

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In order to numerically solve the ordinary differential equation dydt=−y\frac{dy}{dt} = -y for t>0t > 0, with an initial condition y(0)=1y(0) = 1, the following scheme is employedyn+1−ynΔt=−12(yn+1+yn).\frac{y_{n+1} - y_n}{\Delta t} = -\frac{1}{2}(y_{n+1} + y_n).Here, Δt\Delta t is the time step and yn=y(nΔt)y_n = y(n\Delta t) for n=0,1,2,…n = 0, 1, 2, \dots. This numerical scheme will yield a solution with non-physical oscillations for Δt>h\Delta t > h. The value of hh is
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