diff options
Diffstat (limited to 'Part 1/error_script.m')
| -rw-r--r-- | Part 1/error_script.m | 132 |
1 files changed, 76 insertions, 56 deletions
diff --git a/Part 1/error_script.m b/Part 1/error_script.m index 97cc501..8e24418 100644 --- a/Part 1/error_script.m +++ b/Part 1/error_script.m @@ -1,43 +1,8 @@ %-----------------------------------------------------------------
-% clear;
-% ts = 0; % set initial value of x_0
-% is = 0;
-% h = 0.0001; % set step-size
-% tf = 0.03; % stop here
-% R = 0.5;
-% L = 0.0015;
-%
-% A = 6;
-% T = 0.00015;
-%
-% vin = @(t) A * cos(2*pi*t/T);
-% func = @(t, iout) (vin(t) - iout*R) / L; % define func
-% [t, iout ] = midpoint(func, ts, tf, is, h);
-%
-% %numerical solution
-% vout = vin(t) - iout * R;
-%
-% %obtaining the exact solution with favorite method
-% i_Exact = (6/L)*((2*pi)/T * sin((2*pi)/T*t) + (R/L)*cos((2*pi)/T*t) - (R/L)*exp(-(R/L)*t))/((2*pi)/T^2 + (R/L)^2);
-% exact = vin(t) - R*i_Exact;
-%
-% %error as a function of t
-% error = exact - vout;
-%
-% figure(2);
-% plot(t,error); %for midpoint
-% figure(3);
-% t = logspace(-10 ,1);
-% loglog(t,error);
-% grid on;
-
-
-%--------------------------------------------------------------------
-
clear;
ts = 0; % set initial value of x_0
is = 0;
-h = 0.0000005; % set step-size
+h = 0.0001; % set step-size
tf = 0.03; % stop here
R = 0.5;
L = 0.0015;
@@ -47,35 +12,90 @@ T = 0.00015; vin = @(t) A * cos(2*pi*t/T);
func = @(t, iout) (vin(t) - iout*R) / L; % define func
-[t, iout ] = ralston(func, ts, tf, is, h);
+[t, iout ] = midpoint(func, ts, tf, is, h);
-%numerical solution
+%numerical solution
vout = vin(t) - iout * R;
%obtaining the exact solution with favorite method
-i_Exact = @(t) (6/L)*((2*pi)/T * sin((2*pi)/T*t) + (R/L)*cos((2*pi)/T*t) - (R/L)*exp(-(R/L)*t))/((2*pi)/T^2 + (R/L)^2);
-exact = vin(t) - R*i_Exact(t);
+i_Exact = (6/L)*((2*pi)/T * sin((2*pi)/T*t) + (R/L)*cos((2*pi)/T*t) - (R/L)*exp(-(R/L)*t))/((2*pi)/T^2 + (R/L)^2);
+exact = vin(t) - R*i_Exact;
%error as a function of t
-error = abs(exact - vout);
-
-figure(3);
-plot(t,error); %for ralston
+error = exact - vout;
+figure(1);
+plot(t,error); %for midpoint
-max_error = max(error);
+figure(2);
-
-figure(5);
-for k = 1:5
-
- [t, iout] = ralston(func, ts, tf, is, h);
- exact = vin(t) - R*i_Exact(t);
+for ind=3:16 % choose these carefully
+ h1=2^(-ind); % set stepsize
+
+
+ [t, iout] = midpoint(func, ts, tf, is, h1);
+ exact = vin(t) - R*i_Exact(t) ;
vout = vin(t) - R*iout;
- error = abs(exact - vout);
- max_error = max(error);
- plot(log(t), log(max_error),'b*');
- hold on;
- h = 2*h;
+ error = max(abs(exact - vout));
+
+ plot(log(h1),log(error),'b*'); % log/log plot stepsize vs error
+ xlabel({'Time', '(seconds)'});
+ ylabel({'Error'});
+ title('MIDPOINT');
+ hold on; % for next value to be plotted
end
+
+
+%
+% %--------------------------------------------------------------------
+%
+% clear;
+% ts = 0; % set initial value of x_0
+% is = 0;
+% h = 0.0000005; % set step-size
+% tf = 0.03; % stop here
+% R = 0.5;
+% L = 0.0015;
+%
+% A = 6;
+% T = 0.00015;
+%
+% vin = @(t) A * cos(2*pi*t/T);
+% func = @(t, iout) (vin(t) - iout*R) / L; % define func
+% [t, iout ] = ralston(func, ts, tf, is, h);
+%
+% %numerical solution
+% vout = vin(t) - iout * R;
+%
+% %obtaining the exact solution with favorite method
+% i_Exact = @(t) (6/L)*((2*pi)/T * sin((2*pi)/T*t) + (R/L)*cos((2*pi)/T*t) - (R/L)*exp(-(R/L)*t))/((2*pi)/T^2 + (R/L)^2);
+% exact = vin(t) - R*i_Exact(t);
+%
+% %error as a function of t
+% error = abs(exact - vout);
+%
+% figure(3);
+% plot(t,error); %for ralston
+%
+%
+%
+% figure(4);
+%
+% for ind=3:16 % choose these carefully
+% h1=2^(-ind); % set stepsize
+%
+%
+% [t, iout] = ralston(func, ts, tf, is, h1);
+% exact = vin(t) - R*i_Exact(t) ;
+% vout = vin(t) - R*iout;
+% error = max(abs(exact - vout));
+%
+% plot(log(h1),log(error)); % log/log plot stepsize vs error
+% xlabel({'Time', '(seconds)'});
+% ylabel({'Error'});
+% title('V_{out} versus time (original function)');
+% hold on; % for next value to be plotted
+% end
+
+
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