fix exact solution mistake and plot h vs error

1 files changed, 24 insertions, 14 deletions

diff --git a/coursework17/error_script.m b/coursework17/error_script.m
index 5a37fe8..f17f234 100644
--- a/coursework17/error_script.m
+++ b/coursework17/error_script.m
@@ -2,7 +2,8 @@
 R = 0.5;    % 0.5Ohm
 L = 0.0015; % 1.5mH
 
-data_points = 10000;
+data_points = 100000;
+h_divisions = 1000;
 
 % Go on for a time constant
 time_constant = L/R;
@@ -17,24 +18,33 @@ Vin = @(t) A*cos(w_c*t);
 current_initial=0;
 
 % e^m is the integratingn factor
-m = 0.5/0.0015;
+% m = 0.5/0.0015;
 
 % Solution is made by multiplying by integrating factor and
 % then integrating both sides
-current_exact = @(t) 3/(m^2+w_c^2)*(2*m*cos(w_c*t) + 2*w_c*sin(w_c*t));
+
+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;
 
-[time_array, Vout_array] = ralston(R, L, Vin, current_initial, step, data_points*step);
+for k=1:h_divisions
 
-for j=1:data_points
-	error_array(j) = Vout_exact(time_array(j)) - Vout_array(j);
-	% Vout_plot(j) = Vout_exact(time_array(j));
-end
+	[time_array, Vout_array] = ralston(R, L, Vin, current_initial, step*k, data_points*step);
 
-% plot(time_array, Vout_array);
-% figure;
-% plot(time_array, Vout_plot);
-% 
-% max(Vout_plot-Vout_array)
+	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(time_array, error_array);
+loglog(max_t, max_array);