function IterationStepsize
% Function to evaluate how iteration stepsize affects the accuracy
% of the Euler iteration method for two different functions.

% Inputs are read in interactively
% Problem 1 is y = a + b*t assuming we only know dy/dt = b
% and y(0) = a. Pick a = 4 and b = 3.
% Problem 2 is y = a + b*t + c*t^2 assuming we only know dy/dt = b + 2*c*t
% and y(0) = a. Pick a = 4, b = 3, and c = 10.
% Problem 3 is y = a + b*sin(2*pi*t) assuming we only know
% dy/dt = 2*b*pi*cos(2*pi*t)and y(0) = a. Pick a = 4 and b = 3.

% Read inputs
prob = input('Enter number (1, 2 or 3) of problem to be solved: ');
step = input('Enter stepsize in seconds: ');

% Create time vector
t = [0:step:1]';
npts = length(t);
y = zeros(npts,1);
count = 1;

% Perform Euler iteration based on selected problem and stepsize
switch prob
    case 1 % y = a + b*t
        % Define problem constants
        a = 4;
        b = 3;
        
        % Define initial conditions
        y(1,1) = a;
        
        % Perform Euler iteration to produce numerical solution
        for i = 1:npts-1
            dydt = b;
            y(i+1,1) = y(i,1) + dydt*step;
        end
        
        % Plot true and calculated solutions for comparison
        ytrue = a + b*t;
        
        plot(t,ytrue,'k-',t,y,'ro')
        legend('True','Computed')
    case 2 % y = a + b*t+ c*t^2
        % Define problem constants
        a = 4;
        b = 3;
        c = 10;
        
        % Define initial conditions
        y(1,1) = a;
        
        % Perform Euler iteration to produce numerical solution
        for i = 1:npts-1
            dydt = b + 2*c*t(i,1);
            y(i+1,1) = y(i,1) + dydt*step;
        end
        
        % Plot true and calculated solutions for comparison
        ytrue = a + b*t + c*t.*t;
        
        plot(t,ytrue,'k-',t,y,'ro')
        legend('True','Computed')
        
    case 3 % y = a + b*sin(2*pi*t)
        % Define problem constants
        a = 4;
        b = 3;
        
        % Define initial conditions
        y(1,1) = a;
        
        % Perform Euler iteration to produce numerical solution
        for i = 1:npts-1
            dydt = b*2*pi*cos(2*pi*t(i));
            y(i+1,1) = y(i,1) + dydt*step;
        end
        
        % Plot true and calculated solutions for comparison
        ytrue = a + b*sin(2*pi*t);
        
        plot(t,ytrue,'k-',t,y,'ro')
        legend('True','Computed')
        
    otherwise
        fprintf('The problem number entered is incorrect.\n')
        fprintf('Please run the program again.\n')
        return
end