numerical analysis

61 all alll . . . Final-Numerical Fall... An-Najah National University Engineering Numerical Analysis (10626251) Take-home Final Exam - Fall 2020/2021 Please answer all of the following four questions and summarize your results in tables: Problem 1: The temperature of a furnace wall varies with time due to changes in the outside temperature throughout the day are shown in the following table: t (hr) 2 3 5 8 10 15 19 T ( C) 86.5 97.7 104 101.7 92.5 62.3 55 a) Use Newton's third-order polynomial interpolation to find the temperature at time = 11 hr to the best possible accuracy (Note: choose the best data that will minimize the error). b) Using the function found in part a, determine the error in estimating the temperature at time = 8 hrs. c) Find the absolute relative approximate error if the second order polynomial approximation is used instead of the third order for part (a)