Question:
In order to numerically solve the ordinary differential equation \(\frac{dy}{dt}=-y\) for t > 0, with an initial condition y(0) = 1, the following scheme is employed
\(\frac{y_{n+1}-y_n}{\Delta t}=\frac{1}{2}(y_{n+1}+y_n).\)
Here, \(\Delta\)t is the time step and \(y_n = y(n\Delta t)\) for n = 0, 1, 2,…. This numerical scheme will yield a solution with non-physical oscillations for \(\Delta t \gt h\). The value of h is
In order to numerically solve the ordinary differential equation \(\frac{dy}{dt}=-y\) for t > 0, with an initial condition y(0) = 1, the following scheme is employed
\(\frac{y_{n+1}-y_n}{\Delta t}=\frac{1}{2}(y_{n+1}+y_n).\)
Here, \(\Delta\)t is the time step and \(y_n = y(n\Delta t)\) for n = 0, 1, 2,…. This numerical scheme will yield a solution with non-physical oscillations for \(\Delta t \gt h\). The value of h is
\(\frac{y_{n+1}-y_n}{\Delta t}=\frac{1}{2}(y_{n+1}+y_n).\)
Here, \(\Delta\)t is the time step and \(y_n = y(n\Delta t)\) for n = 0, 1, 2,…. This numerical scheme will yield a solution with non-physical oscillations for \(\Delta t \gt h\). The value of h is
Updated On: Jan 23, 2025
- \(\frac{1}{2}\)
- 1
- \(\frac{3}{2}\)
- 2
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The Correct Option is D
Solution and Explanation
The correct option is (D): 4
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