For the following first order ODE, dy dt = y + t for t= 0 to...

  

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For the following first order ODE, dy dt = y + t for t= 0 to t = 1.5 with the initial value of y(0) = 1. This ODE has the analytical solution, y = 7et t-3t-6t-6 Write a MATLAB script to do the following, (a) (4m) Use the function odeEuler to solve using the first order Euler explicit method using h = 0.5. (b) (4m) Write a MATLAB function called odeMidPoint to solve the ODE using the second order mid-point method using h = 0.5. Call this function from your script to solve the ODE. (c) (1m) Use the function odeRK4 to solve using the classical fourth-order Runge-Kutta method using h = 0.5. (d) (3m) Plot the four solutions on a single annotated graph using different markers/colours for the different solutions. (e) (3m) For each method, calculate the mean relative error and the approximate number of accurate digits. For the following first order ODE, dy dt = y + t for t= 0 to t = 1.5 with the initial value of y(0) = 1. This ODE has the analytical solution, y = 7et t-3t-6t-6 Write a MATLAB script to do the following, (a) (4m) Use the function odeEuler to solve using the first order Euler explicit method using h = 0.5. (b) (4m) Write a MATLAB function called odeMidPoint to solve the ODE using the second order mid-point method using h = 0.5. Call this function from your script to solve the ODE. (c) (1m) Use the function odeRK4 to solve using the classical fourth-order Runge-Kutta method using h = 0.5. (d) (3m) Plot the four solutions on a single annotated graph using different markers/colours for the different solutions. (e) (3m) For each method, calculate the mean relative error and the approximate number of accurate digits.

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Given below are the codes and screenshots of the for the functions odeEuler odeMidPoint odeRK4 function ty odeEulerfIy0h ODEEULER Computes the solutio... View the full answer