Consider the ODE: - 7y' (t) 2y(t) = 0 1. Suppose y(t = 0) =...

 

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Consider the ODE: - 7y' (t) — 2y(t) = 0 1. Suppose y(t = 0) = −1, use the Python that you have been developing in tutorials to write a script to calculate Euler's method to approximate y(t) for tЄ [0, 15]. Plot your result against the exact solution. Choose a step-size h, such that Euler's method is clearly stable. (5 Marks) 2. For the same initial conditions, use Improved Euler's method to approximate y(t) for t = [0, 15] and plot your result on the same plot as the Euler result. Choose the same step-size as for Euler's method. (5 Marks) 3. For the same initial conditions, use the classical fourth-order Runge-Kutta method to approximate y(t) for tЄ [0, 15] and plot your result on the same plot as the Euler result. Choose the same step-size as for Euler's method. (5 Marks) Consider the ODE: - 7y' (t) — 2y(t) = 0 1. Suppose y(t = 0) = −1, use the Python that you have been developing in tutorials to write a script to calculate Euler's method to approximate y(t) for tЄ [0, 15]. Plot your result against the exact solution. Choose a step-size h, such that Euler's method is clearly stable. (5 Marks) 2. For the same initial conditions, use Improved Euler's method to approximate y(t) for t = [0, 15] and plot your result on the same plot as the Euler result. Choose the same step-size as for Euler's method. (5 Marks) 3. For the same initial conditions, use the classical fourth-order Runge-Kutta method to approximate y(t) for tЄ [0, 15] and plot your result on the same plot as the Euler result. Choose the same step-size as for Euler's method. (5 Marks)