Gregory-Newton formulas forward

In this section, we will develop two interpolation methods for equally spaced data (I) the Gregory-Newton formulas, which are based on forward and backward differences, and (2) Stirling s interpolation formula, based on central differences. 

The Gregory-Newton forward interpolation formula can be derived using the forward finite difference relations derived in Secs. 3.2 and 3.4. Eq. (3.17), written for the function/... 

This is the Gregory-Newton forward interpolation formula. The general formula of the above... 

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. 

Method of Solution The function uses the general formula of the Gregory-Newton forward interpolation [Eq. (3.123)] to perform the n-order interpolation. The input to the function specifying the number of base points must be at least (n + 1). 

Solution to Example 3.1. It interpolates the time-temperature data % given in Table E3.1 by Gregory-Newton forward interpolation % formula and finds the maximum temperature and the time this % maximum happened. 

This method is accomplished by first replacing the function y = f x) with a polynomial approximation, such as the Gregory-Newton forward interpolation formula [Eq. (3.122)], In practice, the interval [x, x ] is being divided into several segments, each of width h, and the Gregory-Newton forward interpolation formula becomes note that =x + h) ... 

These values give the best interpolation at t = 575°F rather than the Newton-Gregory s forward or backward interpolation formulae. 

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