% This script will carry out error analysis
R = 0.5;    % 0.5Ohm
L = 0.0015; % 1.5mH

data_points = 100000;
h_divisions = 1000;

% Go on for a time constant
time_constant = L/R;
step = time_constant/data_points;

T=150e-6; % 150us
f = 1/T;  
w_c = 2*pi*f;
A = 6;

Vin = @(t) A*cos(w_c*t);
current_initial=0;

% e^m is the integratingn factor
% m = 0.5/0.0015;

% Solution is made by multiplying by integrating factor and
% then integrating both sides

A = 6*R/(R^2 + (w_c*L)^2);
B = 6*w_c*L/(R^2 + (w_c*L)^2);

current_exact = @(t) A*cos(w_c*t) + B*sin(w_c*t) - A*exp((-R/L)*t);
%current_exact = @(t) 3/(m^2+w_c^2)*(2*m*cos(w_c*t) + 2*w_c*sin(w_c*t));
Vout_exact = @(t) Vin(t) - current_exact(t)*R;

for k=1:h_divisions

	[time_array, Vout_array] = ralston(R, L, Vin, current_initial, step*k, data_points*step);

	for j=1:data_points/k
		error_array(j) = Vout_exact(time_array(j)) - Vout_array(j);
		% Vout_plot(j) = Vout_exact(time_array(j));
	end

	% plot(time_array, Vout_array);
	% figure;
	% plot(time_array, Vout_plot);
	% 
	max_array(k) = max(error_array);
	max_t(k) = k*step;
end

loglog(max_t, max_array);