Question

(PLEASE COMPLETE EACH PART OF THE QUESTION , WITH FULL WORKING THANK YOU)

QUESTION 4 Consider a car driving along a road, which has a traction force and a drag force acting on it. We can model the car with the ODE v'(t) m where v(t) is the velocity of the car, F, is the traction force and k is a drag coefficient. Given m 1000, Fi = 10000e, k 0.5 and v(0) 0, 13.63 (a) Use Euler's Method to approximate v(2) using a step size ofh 1. Ans: v(2) (b) Use Modified Euler's Method to approximate v(2) using a step size of h = 1. Ans: v(2) 9.29 (c) Which approximate for v(2) would you expect to be more accurate? Explain why. Ans: Modified Euler since it's a higher order method. (d) Explain what effect reducing step size would have on the accuracy of the numerical so- lution. Ans: Reducing step size will typically improve the accuracy of the numerical solution

Answer 1

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