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Using the RK4 method, give the numerical approximation for the IVP: y' ty; 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 ki values to approximate this ODE)?. 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.

Using the RK4 method, give the numerical approximation for the IVP: y' ty; 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 ki values to approximate this ODE)?. 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.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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since I am not too good with matlab help me out 

You are to create a script in Matlab that will estimate the solution for an ordinary differ- ential equation using the RK4 method outlined above. Below is some code to help you get started: %RK4 clearvars %always helpful to have so matlab doesn’t remember past things! @(t,y) (-2*t*y^2); %define function, e.g. your y' f = %the initial conditions yo 1; %3D t0 = 0; Q_val 1; %define query point %3D h = .5; %step size iterationN round ( (Q_val-t0)/step); %helpful if your IVP is not at t=0. %3D = zeros (iterationN+1, 1); %initalize empty vector for y values yi ti = zeros (iterationN+1,1); %initialize empty vector for t values %placing IVP into yi and xi vectors yi (1) 3D у0; ti(1) t0; %3D
Transcribed Image Text:You are to create a script in Matlab that will estimate the solution for an ordinary differ- ential equation using the RK4 method outlined above. Below is some code to help you get started: %RK4 clearvars %always helpful to have so matlab doesn’t remember past things! @(t,y) (-2*t*y^2); %define function, e.g. your y' f = %the initial conditions yo 1; %3D t0 = 0; Q_val 1; %define query point %3D h = .5; %step size iterationN round ( (Q_val-t0)/step); %helpful if your IVP is not at t=0. %3D = zeros (iterationN+1, 1); %initalize empty vector for y values yi ti = zeros (iterationN+1,1); %initialize empty vector for t values %placing IVP into yi and xi vectors yi (1) 3D у0; ti(1) t0; %3D
Using the RK4 method, give the numerical approximation for the IVP: y' ty; 0.5 for the point at t = 20. How does this compare to Euler's Method (e.g. simply using the ki values to approximate this ODE)?. y(0) = e; with a step size of h 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.
Transcribed Image Text:Using the RK4 method, give the numerical approximation for the IVP: y' ty; 0.5 for the point at t = 20. How does this compare to Euler's Method (e.g. simply using the ki values to approximate this ODE)?. y(0) = e; with a step size of h 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.
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