15. Compare the performance of Euler's method, one of the...

15. Compare the performance of Euler's method, one of the second-order Runge- Kutta methods, and the classical fourth-order Runge-Kutta method on the initial value problem $\frac{dx}{dt} = \frac{t}{x}$ $(0 \le t \le 5)$, $x(0) = 1$. (5) The exact solution for this problem is $x(t) = \sqrt{t^2 + 1}$.

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Text: Section 7.4: #15. Use your Matlab scripts for Euler's method, Modified Euler's method, and the classical RK4 method. You will need to write a script that implements the classical RK4 method. We will talk more about this method on Thursday, and you may have some time in class to work on it. You should demonstrate the global error by making a log-log plot of the error at the final time vs. several values of h similar to previous homework assignments. You should also compare the performance by creating a plot which shows the difference between each approximate solution and the exact solution, i.e. |w - y|, as a function of t. 15. Compare the performance of Euler's method, one of the second-order Runge-Kutta methods, and the classical fourth-order Runge-Kutta method on the initial value problem MSRTT dx/dt = T(0,t)5x(0)=1.x The exact solution for this problem is x(t) = Vt^2 + i.

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