[Numerical Analysis] [MATLAB]

Requires MATLAB

1. Solve the initial value problem using MATLAB

() = e^t sin(e^t 1), (0) = 0,

on [0, 2], using the forward Euler method. Note that you need also to adjust the forward Euler code to reflect the function being only dependent on t, not y.

You should run your code with = 21, 51, 101, and 201 to make sure it converges. Plot the four curves on one graphing display with "hold" command. Use different colors and line characters so that each curve has a unique signature.

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Does NOT require Matlab

Show that:

| [((₊₃) 9(₊₁) + 8())/ 6] () | = (²).

2. Using the step size t = 0.5, approximate the solution y(t) at t = 0.5 to an initial value problem

() = sin( 1), (0) = 0,

using the forward Euler method.