Consider the IVPS f(t,y), astb, y(a)=a. dt dy -12y, Ost1, y(0)=1. (1) (2) 1. Write a...

 

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Consider the IVPS f(t,y), astb, y(a)=a. dt dy -12y, Ost1, y(0)=1. (1) (2) 1. Write a Matlab function called RK2 that solve (1) using Order 2 Runge-Kutta method. Use this method to solve the IVP (2) with N 20, 50, 100. Call yo, y1, y2, the three results and plot the three solutions on the same graph. Make a loglog plot of absolute error at t=1 versus the number of intervals for all three methods on the same plot. Compare the solution at t = 1 with the exact solution at t = 1. Create Err a vector that stores the absolute error of the three solutions at t = 1. Comment on the result (is the method converging or not, etc.) using \. Consider the IVPS f(t,y), astb, y(a)=a. dt dy -12y, Ost1, y(0)=1. (1) (2) 1. Write a Matlab function called RK2 that solve (1) using Order 2 Runge-Kutta method. Use this method to solve the IVP (2) with N 20, 50, 100. Call yo, y1, y2, the three results and plot the three solutions on the same graph. Make a loglog plot of absolute error at t=1 versus the number of intervals for all three methods on the same plot. Compare the solution at t = 1 with the exact solution at t = 1. Create Err a vector that stores the absolute error of the three solutions at t = 1. Comment on the result (is the method converging or not, etc.) using \.