MATLAB data interpolation

These indicate the limit of our successful numerical BVP integrations near the bifurcation points. In between the x and o marks on the middle branch, the curve is drawn using interpolation of our successful BVP solutions data, while in between two adjacent x or two adjacent o marks, the curve is drawn by extrapolating nearby computed function data. This is done automatically by MATLAB s plot commands. 

An exothermic, relatively slow reaction takes place in a reactor under your supervision. Yesterday, after you left the plant, the temperature of the reactor went out of control, for a yet unknown reason, until the operator put it under control by changing the cooling water flow rate. Your supervisor has asked you to prepare a report regarding this incident. As the first step, you must know when the reactor reached its maximum temperature and what was the value of this maximum temperature. A computer was recording the temperature of the reactor at one-hour intervals. These time-temperature data are given in Table E3.1. Write a general MATLAB function for -order one-dimensional interpolation by Gregory-Newton forward interpolation formula to solve this problem. 

Write a MATLAB function that uses the Gregory-Newton backward interpolation formula to evaluate the function f x) from a set of (n + I) equally spaced input values. Write the function in a general fashion so that n can be any positive integer. Also write a MATLAB script that reads the data and shows how this MATLAB function fits the data. Use the experimental data of Table 3.3 to verify the program, and evaluate the function atx= 10, 50,90,130, 170, and 190. 

Between Reynolds niunbers of 350000 and 1000000, there is a transient drop in the drag constant as the boundary layer first becomes turbulent, delaying separation on the downstream side. In this regime, we may use interpolation (MATLAB function interpi) of the data in Table 2.2. 

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