ME3255_HW3_convergance.m

%ME3255 Homework 3
%Ryan Hyatt
%See README.m
%TODO - A better description.

clc

vmag = 5; %input initial speed.
height = 1.27; %target height.
y0 = 1.72; %the initial height of the projectile.
a = -9.81; %downward acceleration due to gravity.
delta_x = 2.37; %horizontal displacement

es = .00001;%accuracy?
dx = 10e-6;
maxiter = 10000;
xrold = 0;


guess = 25; % value of initial guess, if the function requires one.

thetas = linspace(15,65);
heights = ones(1,length(thetas));
i = 0;

for i = 1:length(thetas)
    heights(i) = projectile(thetas(i), vmag)-height;
end

plot(thetas, heights)

for maxiter = 1:50

    %Newton's method.
    [root(maxiter,1),ea(maxiter,1),iter(1)] = newtraph(@(theta) projectile(theta, vmag) - height,...
        @(theta) dprojectile_dtheta(theta, vmag),...
        guess,es,maxiter); % 1

    %False Position Method
    xl = 0;
    xu = 30;

    [root(maxiter,2),fx,ea(maxiter,2),iter(2)]=falsepos(@(theta) (projectile(theta, vmag) - height)...
        ,xl,xu,es,maxiter); %2

    %Bisect Method
    [root(3),fx,ea(3),iter(3)]=bisect(@(theta) (projectile(theta, vmag) - height)...
	,xl,xu,es,maxiter); %3
    
    
    
    %Modified Secant
    [root(maxiter,4),ea(maxiter,4),iter(4)]=mod_secant(@(theta) (projectile(theta, vmag) - height),...
       dx,guess,es,maxiter); %4
    
end

ea

plot(ea)
title('Convergance');
xlabel('Iterations');
ylabel('ea');