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AE5139HW1

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Aug 25th, 2019
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  1. % AE 5139 Intro to CFD
  2. % Homework 1
  3. % Due: 27 Aug 2019
  4. % Christopher Bates
  5. % Pastebin Link:
  6.  
  7. clear all
  8. close all
  9. clc
  10.  
  11. dx           = [0.1, 0.01];
  12. x0           = 0;
  13. xmax         = 3;
  14.  
  15. syms x
  16. dydx         = @(x) x^2 + tanh(x);  
  17. y            = @(x) (1/3)*x^3 + log(cosh(x));
  18.  
  19.  
  20. Error = zeros(2);
  21.  
  22. i = 0;
  23.  
  24. for k = dx
  25.     i = i+1;
  26.    
  27.    X = x0:dx(i):xmax;
  28.    
  29.    [numRows, numElems] = size(X);
  30.    
  31.    y_apx = zeros(numElems);
  32.    
  33.    y_apx(1) = 0 + dydx(X(1)) * dx(i);
  34.    
  35.    for j = 2:numElems
  36.        
  37.        y_apx(j) = y_apx(j-1) + dydx(X(j-1)) * dx(i);
  38.        
  39.        if j == numElems
  40.            figure
  41.            plot(X,y_apx)
  42.            xlabel('x-axis','Interpreter','latex')
  43.            ylabel('y-axis','Interpreter','latex')
  44.            mytitleText = ['Approximate value of integral for \Deltax = ',num2str(dx(i))];
  45.            title(mytitleText,'Interpreter','tex' );
  46.            
  47.            Error(i) = (y(xmax) - y_apx(numElems)) / y(xmax);
  48.        end
  49.    end
  50.    
  51.    if i == 1
  52.        ValueTable = table(X',y_apx);
  53.        ValueTable.Properties.VariableNames = {'x','y'};
  54.        writetable(ValueTable,'ValueTable.txt')
  55.    end
  56. end
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