AE5139HW1

% AE 5139 Intro to CFD
% Homework 1
% Due: 27 Aug 2019
% Christopher Bates
% Pastebin Link:

clear all
close all
clc

dx           = [0.1, 0.01];
x0           = 0;
xmax         = 3;

syms x
dydx         = @(x) x^2 + tanh(x);
y            = @(x) (1/3)*x^3 + log(cosh(x));


Error = zeros(2);

i = 0;

for k = dx
    i = i+1;

   X = x0:dx(i):xmax;

   [numRows, numElems] = size(X);

   y_apx = zeros(numElems);

   y_apx(1) = 0 + dydx(X(1)) * dx(i);

   for j = 2:numElems

       y_apx(j) = y_apx(j-1) + dydx(X(j-1)) * dx(i);

       if j == numElems
           figure
           plot(X,y_apx)
           xlabel('x-axis','Interpreter','latex')
           ylabel('y-axis','Interpreter','latex')
           mytitleText = ['Approximate value of integral for \Deltax = ',num2str(dx(i))];
           title(mytitleText,'Interpreter','tex' );

           Error(i) = (y(xmax) - y_apx(numElems)) / y(xmax);
       end
   end

   if i == 1
       ValueTable = table(X',y_apx);
       ValueTable.Properties.VariableNames = {'x','y'};
       writetable(ValueTable,'ValueTable.txt')
   end
end