ASSIGNMENT 3: ODE Solve the following problem over the interval from t = 0 to 3 using a step size of 0.5 where y(0) = 1 dy = yt? - 1.ly dt 1) using analytical solution 2) Compare your solutions using (a) Euler's (b) Heun's (c) RK-4 Write the answer according to the exam template. Show 2 iterations with detail calculation and complete the table. 1) Analytical solution. Show the derivation of y equation. t Ytrue 0 1
a) Euler's Method Iteration 1: Iteration 2: i t Ytrue k у & %) 0 0 1 1 2 3 4 5 6
b) Heun's Method Iteration 1: Iteration 2: i t Ytrue k1 k2 y Et (%) 0 0 1 1 2 3 4 5 6
a) RK-4 Method Iteration 1: Iteration 2: i t Ytrue ki k2 k3 k4 у & (%) 0 0 1 1 2 3 4 5 6