hw7_solutions

hw7_solutions - MAE 107 Spring 2007 HW 7 Problem 1 This...

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Unformatted text preview: MAE 107 Spring 2007 HW 7 Problem 1 This code interpolates the given data for the conductivity-temperature function, and evaluates this function at x = 4. Contents Setup (a) Forward Difference Table (b) Construct Newton-Gregory Polynomial (c) Using Direct MATLAB Commands Optimal fit Setup clear; close all ; clc % input data point h = 0.4; % data interval % temperature x = 1:h:5; % conductivity f = [1.210 1.1968 1.2999 1.4378 1.6183 1.849 2.1376 2.4919 2.9194 3.427 4.025]; (a) Forward Difference Table n = size(x,2); % data poi nts (=11) % construct the table table(1,:) = x; table(2,:) = f; for i = 3:n+1 table(i,1:n-i+2) = diff(table(i-1,1:n-i+3)); %diff(c)=[c(2)-c(1), c(3)-c(2), ..., c(n)- c(n-1)] end fprintf( 'The forward difference table:\n' ) table = table'; disp(table) The forward difference table: Columns 1 through 9 1.0000 1.2100 -0.0132 0.1163 -0.0815 0.0893 -0.0895 0.0898 -0.0901 1.4000 1.1968 0.1031 0.0348 0.0078 -0.0002 0.0003 -0.0003 -0.0001 1.8000 1.2999 0.1379 0.0426 0.0076 0.0001 -0.0000 -0.0004 0.0005 2.2000 1.4378 0.1805 0.0502 0.0077 0.0001 -0.0004 0.0001 0.0042 2.6000 1.6183 0.2307 0.0579 0.0078 -0.0003 -0.0003 0.0043 0 3.0000 1.8490 0.2886 0.0657 0.0075 -0.0006 0.0040 0 0 3.4000 2.1376 0.3543 0.0732 0.0069 0.0034 0 0 0 3.8000 2.4919 0.4275 0.0801 0.0103 0 0 0 0 4.2000 2.9194 0.5076 0.0904 0 0 0 0 0 4.6000 3.4270 0.5980 0 0 0 0 0 0 5.0000 4.0250 0 0 0 0 0 0 0 Columns 10 through 12 0.0900 -0.0894 0.0925 0.0006 0.0031 0 0.0037 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (b) Construct Newton-Gregory Polynomial x0 = 1; % in order to have degree 10 polynomial, one has to start at x0 = 1 s = (4-x0)/h;...
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hw7_solutions - MAE 107 Spring 2007 HW 7 Problem 1 This...

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