1. [20 marks] Answer in a separate book marked Ques- tion 1 Explain the differen
ID: 3283607 • Letter: 1
Question
1. [20 marks] Answer in a separate book marked Ques- tion 1 Explain the difference between Interpolation and Curve Fitting meth- ods. Give an example where curve fitting would be more useful than interpolation. ii) For the following data x = 0.0 0.5 1.0 1.5 2.0 2.5 v = 8.0 9.1 9.7 9.5 8.1 5.0 b) (1) Determine the location and magnitude of the maximum value of v using quadratic interpolation. (2) Using both trapesoidal and Simpson's rule, evaluate average value of v = 25 S. v dx. Explain the differences between your results. i) Compute forward and central difference approximations for the first derivative of f(x) = x - 1/In(x) at x = 4 using a value of Ax = 0.5. ii) Calculate the percentage relative errors for each approximation by comparing with exact solution and discuss your results. What would you suggest to decrease the error in both approximations? Which finite difference approximation is normally used for the second derivative of f(x)? Compute the second derivative using this finite difference approximation and compare with exact solution. The exact solution is: f'(4) = 0.05, f"(4) = 0.0625.Explanation / Answer
Curve-fitting is when you have a dataset of scattered points and find a line (or curve) that best fits the general shape of the data.
Interpolation is when you have two points of data and want to know what a value between the two would be. Half way between would be their average, but if you want to know only a quarter of the way between the two you'd have to interpolate.
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