Using Matlab to solve the following question:
Provide a labeled graph of the solution of the initial value problem.
The exact solution is, of course, y(t) = e^st, with s = 1 s^-1 (The constant s in the exponent is the real frequency, here 1 neper (dimensionless) per second. Real frequencies represent growth or decay, depending on sign. The last problem had an imaginary frequency of f Hertz, or cycles per second, representing periodicity. Imaginary frequencies are the periodic, sinusoidal part, and there is none here.
Always check to make sure the argument of a transcendental function is dimensionless! With t in seconds and s in 1/seconds, st is dimensionless.)
You need to provide multiple graphs on one set of axes from t=0 to t=5 seconds (on one page) clearly labeled by your Matlab code:
1. The exact solution.
2. Four solutions integrated numerically using Euler's forward method, the simplest algorithm there is for simulating differential equations: (click for example)
1. Start at the differential equation's initial value (in this case, y(0) = 1)
2. Use the slope from the differential equation at that point to find the rise to the next point; add the initial value and graph that line
3. Repeat using the endpoint of the line from 2.
4. Stop at the maximum graph point desired.
3. The four integrated solutions should represent repeated halvings of the Euler interval:
1. The first solution should go from t=0 to t=5 in one step
2. The second solution should span that in two steps.
3. The third solution should span it in four steps.
4. The fourth solution should span it in eight steps.
