finish exact solution

1 files changed, 13 insertions, 6 deletions

diff --git a/coursework17/error_script.m b/coursework17/error_script.m
index 2744ba9..08a42d2 100644
--- a/coursework17/error_script.m
+++ b/coursework17/error_script.m
@@ -6,21 +6,28 @@ data_points = 10000;
 
 % Go on for 8 time constants
 time_constant = L/R;
-step = time_constant*8/data_points;
+step = time_constant/data_points;
 
 T=150e-6; % 150us
 f = 1/T;  
+w_c = 2*pi*f;
+A = 6;
 
-Vin = @(t) 6*cos(2*pi*f*t);
+Vin = @(t) A*cos(w_c*t);
 current_initial=0;
 
-current_exact = @(t) --
-Vout_exact = @(t) --
+% e^m is the integratingn factor
+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));
+Vout_exact = @(t) Vin(t) - current_exact(t)*R;
 
 [time_array, Vout_array] = ralston(R, L, Vin, current_initial, step, data_points*step);
 
 for j=1:data_points
-	error_array(j) = Vout_exact(time_array(j)) - Vout_aray(j);
+	error_array(j) = Vout_exact(time_array(j)) - Vout_array(j);
 end
 
-plot(log(time_array),log(error_array));
+loglog(time_array, error_array);