1. Using the RK4 method, give the numerical approximation for the IVP: y' y(0)=e; with a...

 

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1. Using the RK4 method, give the numerical approximation for the IVP: y' y(0)=e; with a step size of h = 0.5 for the point at t = 20. How does this compare to Euler's Method (e.g. simply using the k values to approximate this ODE)?. 2. The exact solution to the IVP above is y(t) = et/2+1. In a single figure, plot the results of RK4, Euler methods and the exact function (thus, your plot should contain 3 lines). To show the full Y-range, the Y-axis should be plotted using a log-scale, however the X-axis should remain linear. To do this, type "set(gca, 'YScale', 'log')" on the line below that used to create the plot. Make sure that your figure has a legend that describes what each line corresponds to. 1. Using the RK4 method, give the numerical approximation for the IVP: y' y(0)=e; with a step size of h = 0.5 for the point at t = 20. How does this compare to Euler's Method (e.g. simply using the k values to approximate this ODE)?. 2. The exact solution to the IVP above is y(t) = et/2+1. In a single figure, plot the results of RK4, Euler methods and the exact function (thus, your plot should contain 3 lines). To show the full Y-range, the Y-axis should be plotted using a log-scale, however the X-axis should remain linear. To do this, type "set(gca, 'YScale', 'log')" on the line below that used to create the plot. Make sure that your figure has a legend that describes what each line corresponds to.