HW3_Script.m

%HW_3
%Script calls functions and outputs tables and plots relevant to HW3.

 [root1,fx1,ea1,iter1]=falsepos(@(x) projectile(x),1,50,.00001);
 [root2,ea2,iter2]=mod_secant(@(x) projectile(x),1,50,.00001);
 [root3, ea3, iter3]= newtraph(@(x) projectile(x),@(x) dprojectile_dtheta(x),50,.00001,1000);
 [root4,fx4,ea4,iter4]=bisect(@(x) projectile(x),0,50,.00001);


 %Question 1: part (i)
 %for loop creates data table for given outputs above 
for n=1:4;
    Table(n,1)=root(n);
    Table(n,2)=ea(n);
    Table(n,3)=iter(n);
    Table(n,4)=fx(n);
end


%Question 1: part(ii)
%Plots the graphs that compare methods
e_b = 1;
e_f = 2;
e_n = 3;
e_m = 4;
    for n = 1:iter1
        [r, y, e_b(n), k] = falsepos(@(x) projectile(x),1,50,.00001);
    end
    
    for n = 1:iter2
        [r, y, e_f(n)] = mod_secant(@(x) projectile(x),1,50,.00001);
    end
    
    for n = 1:iter3
        [r, e_n(n), k] = newtraph(@(x) projectile(x),@(x) dprojectile_dtheta(x),50,.00001,1000);
    end
    
    for n = 1:iter4
        [r, e_m(n), k] = bisect(@(x) projectile(x),0,50,.00001);
    end
    
 %Plot
 %This section sets up the code inorder to plot the data.
    
    setdefaults
    plot(1:iter1, e_b, 'g', 1:iter2, e_f, 'b', 1:iter3, e_n, 'r', 1:iter4, e_m, 'y')
    title('Approx Err. of Convergent Functions vs Number of Iterations');
    xlabel('Iteration');
    ylabel('Approx Error');
    legend('bisect','falsepos', 'newtraph', 'mod secant');