You are given an analytic solution for three flows as follows: Flow 1: y = sin...

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You are given an analytic solution for three flows as follows: Flow 1: y = sin (x) Flow 2: y = x Flow 3: y = x² You aim to understand how accurately you can approximate the derivative using finite differences. Evaluate the numerical error compared to the analytic solution (by differentiating the above eqn) as a function of mesh size Ax. (a) For the first derivative using a 1st and 2nd order Finite difference (b) For the second derivative using a 1st and 2nd order Finite difference (c) Which mesh size yields roughly 5% accuracy? You are given an analytic solution for three flows as follows: Flow 1: y = sin (x) Flow 2: y = x Flow 3: y = x² You aim to understand how accurately you can approximate the derivative using finite differences. Evaluate the numerical error compared to the analytic solution (by differentiating the above eqn) as a function of mesh size Ax. (a) For the first derivative using a 1st and 2nd order Finite difference (b) For the second derivative using a 1st and 2nd order Finite difference (c) Which mesh size yields roughly 5% accuracy?

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SOLUTION To calculate the numerical error we first need to calculate the finite difference approximations for the first and second derivatives a First ... View the full answer