Problem 2: Assume that y(t) = 4 cost - 7(t-4) is the solution to some initial...

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Problem 2: Assume that y(t) = 4 cost - 7(t-4) is the solution to some initial value problem on -2 t 3. a) Calculate the local truncation error when Euler's method is applied to this problem. Derive an upper bound for the local truncation error at t = 3 if the stepsize is h = 0.001. b) For the same function y(t), and also for h = 0.001, find an upper bound for the global error for Euler's method at t = 3, if we assume that the Lipschitz constant is L = 2. You would likely get a bigger number than the local truncation error. Problem 2: Assume that y(t) = 4 cost - 7(t-4) is the solution to some initial value problem on -2 t 3. a) Calculate the local truncation error when Euler's method is applied to this problem. Derive an upper bound for the local truncation error at t = 3 if the stepsize is h = 0.001. b) For the same function y(t), and also for h = 0.001, find an upper bound for the global error for Euler's method at t = 3, if we assume that the Lipschitz constant is L = 2. You would likely get a bigger number than the local truncation error.

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