Question: (a) (b) An initial value problem 4er-0.5y:y(0)-2. i) dt i) Approximate y(2) using two-step Euler's method. (3 marks) Given that the exact solution is

(a) (b) An initial value problem 4er-0.5y:y(0)-2. i) dt i) Approximate y(2)

(a) (b) An initial value problem 4er-0.5y:y(0)-2. i) dt i) Approximate y(2) using two-step Euler's method. (3 marks) Given that the exact solution is y=3.0769(ees)+2e05. Calculate the relative error. (3 marks) 0.25 68.11 Consider the initial value problem y*=9.81- Rewrite the initial value problem into a pair of first order differential equations. (1 mark) y' with x(0)= y(0)=0. From the answer in (b)(i), approximate the solution of y at x=2 using one- step fourth order Runge-Kutta method. Four values of the Ks are given as K=0,K=9.81, K, -9.81 and K2=9.4567. (10 marks)

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