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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! f = @(t,y) (-2*t*y^2); %define function, e.g. your y' %the initial conditions yo = 1; to = 0; Q_val= 1; %define query point h = .5; %step size iterationN = round ((Q_val-t0)/step); %helpful if your IVP is not at t=0. yi = zeros(iterationN+1, 1); %initalize empty vector for y values ti = zeros(iterationN+1,1); %initialize empty vector for t values %placing IVP into yi and xi vectors yi (1) = y0; ti(1) = to; From here you need to implement a for loop to approximate the solution.

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! f = @(t,y) (-2*t*y^2); %define function, e.g. your y' %the initial conditions yo = 1; to = 0; Q_val= 1; %define query point h = .5; %step size iterationN = round ((Q_val-t0)/step); %helpful if your IVP is not at t=0. yi = zeros(iterationN+1, 1); %initalize empty vector for y values ti = zeros(iterationN+1,1); %initialize empty vector for t values %placing IVP into yi and xi vectors yi (1) = y0; ti(1) = to; From here you need to implement a for loop to approximate the solution.

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
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Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Suppose we have the initial value problem (IVP): y = f(t,y); y(to) = Yo y is an unknown function where y is the time derivative of the function y, i.e. y = of time t, which we would like to approximate; we are told that y, the rate at which y changes, is a function of t and of y itself. At the initial time to the corresponding y value is yo. The function f and the data to, yo are given. We want to 'step' through the function to find a numerical approximation at some time, t. Choose a step size, h, such that h> 0 and define: for n = 0, 1, 2, 3,..., using: Yn+1 = Yn +(k₁ + 2k₂ + 2k³+k₁) $n+1=t+h k₁= f(tn, yn) k₂ = f (tn + 1/3, yn + /2k1) Yn k3 = f(tn + 1/2, Yn + 1/2k2) 1 k₁ = f(tn+h, Yn + hk3) Here yn+1 is the RK4 approximation of y(tn+1), and the next value (n+1) is determined by the present value (yn) plus the weighted average of four increments, where each increment is the product of the size of the interval, h, and an estimated slope specified by function f on the right-hand side of the differential equation. • k₁ is the increment based on the slope at the beginning of the interval, using y. • k₂ is the increment based on the slope at the midpoint of the interval, using y + 2k₁; k3 is again the increment based on the slope at the midpoint, but now using y + k₂; • k₁ is the increment based on the slope at the end of the interval, using y + hk3.
Transcribed Image Text:Suppose we have the initial value problem (IVP): y = f(t,y); y(to) = Yo y is an unknown function where y is the time derivative of the function y, i.e. y = of time t, which we would like to approximate; we are told that y, the rate at which y changes, is a function of t and of y itself. At the initial time to the corresponding y value is yo. The function f and the data to, yo are given. We want to 'step' through the function to find a numerical approximation at some time, t. Choose a step size, h, such that h> 0 and define: for n = 0, 1, 2, 3,..., using: Yn+1 = Yn +(k₁ + 2k₂ + 2k³+k₁) $n+1=t+h k₁= f(tn, yn) k₂ = f (tn + 1/3, yn + /2k1) Yn k3 = f(tn + 1/2, Yn + 1/2k2) 1 k₁ = f(tn+h, Yn + hk3) Here yn+1 is the RK4 approximation of y(tn+1), and the next value (n+1) is determined by the present value (yn) plus the weighted average of four increments, where each increment is the product of the size of the interval, h, and an estimated slope specified by function f on the right-hand side of the differential equation. • k₁ is the increment based on the slope at the beginning of the interval, using y. • k₂ is the increment based on the slope at the midpoint of the interval, using y + 2k₁; k3 is again the increment based on the slope at the midpoint, but now using y + k₂; • k₁ is the increment based on the slope at the end of the interval, using y + hk3.
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! f = @(t,y) (-2*t*y^2); %define function, e.g. your y' %the initial conditions yo = 1; to = 0; Q_val = h = .5; %step size iterationN- round ((Q_val-t0)/step); %helpful if your IVP is not at t=0. yi = zeros(iterationN+1, 1); %initalize empty vector for y values ti = zeros(iterationN+1,1); %initialize empty vector for t values %placing IVP into yi and xi vectors yi (1) 1; %define query point yo; ti(1) - to; From here you need to implement a for loop to approximate the solution.
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! f = @(t,y) (-2*t*y^2); %define function, e.g. your y' %the initial conditions yo = 1; to = 0; Q_val = h = .5; %step size iterationN- round ((Q_val-t0)/step); %helpful if your IVP is not at t=0. yi = zeros(iterationN+1, 1); %initalize empty vector for y values ti = zeros(iterationN+1,1); %initialize empty vector for t values %placing IVP into yi and xi vectors yi (1) 1; %define query point yo; ti(1) - to; From here you need to implement a for loop to approximate the solution.
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