Add files via upload

8 files changed, 206 insertions, 71 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

+

+

diff --git a/Part 1/error_script_heun.m b/Part 1/error_script_heun.m
index 8c0f49f..8e2dff3 100644
--- a/Part 1/error_script_heun.m
+++ b/Part 1/error_script_heun.m
@@ -18,14 +18,28 @@ func = @(t, iout) (vin(t) - iout*R) / L;      % define func
 vout = vin(t) - iout * R;

 

 %obtaining the exact solution with favorite method

-i_{Exact} = (V_{initial_in}/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};

+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= exact - vout; 

+error = abs(exact - vout); 

 

 figure(1);

 plot(t,error); %for heun

-loglog(error);

+%loglog(error);

+

+figure(5);

+for ind=3:16 % choose these carefully

+ h1=2^(-ind); % set stepsize

+ 

+ 

+    [t, iout] = heun(func, ts, is, h1);

+    exact = vin(t) - R*i_Exact(t)  ;

+    vout = vin(t) - R*iout;

+    error = max(abs(exact - vout)); 

+    

+    plot(log(h1),log(error),'b*'); % log/log plot stepsize vs error

+    hold on; % for next value to be plotted

+end

 

 end

 

diff --git a/Part 1/exact_solution.m b/Part 1/exact_solution.m
new file mode 100644
index 0000000..4cd8902
--- /dev/null
+++ b/Part 1/exact_solution.m
@@ -0,0 +1,9 @@
+function [ t, i_Exact ] = exact_solution(R,L,T,tfinal, h)

+

+N = round((tfinal) / h);

+t = zeros(1,N);

+i_Exact = zeros(1,N);

+for i = 1 : N - 1

+    t(i+1) = t(i) + h;

+    i_Exact(i+1) = (6/L)*((2*pi)/T * sin((2*pi)/T*t(i)) + (R/L)*cos((2*pi)/T*t(i)) - (R/L)*exp(-(R/L)*t(i)))/((2*pi)/T^2 + (R/L)^2);

+end

diff --git a/Part 1/heun_temp.m b/Part 1/heun_temp.m
new file mode 100644
index 0000000..9a49d4a
--- /dev/null
+++ b/Part 1/heun_temp.m
@@ -0,0 +1,13 @@
+function [y, t] = heun_temp(f,a,b,ya,n)

+h = (b - a) / n;

+halfh = h / 2;

+y(1,:) = ya;

+t(1) = a;

+for i = 1 : n

+    t(i+1) = t(i) + h;

+    g = f(t(i),y(i,:));

+    z = y(i,:) + h * g;

+    y(i+1,:) = y(i,:) + halfh * ( g + f(t(i+1),z) );

+end;

+

+%func,t0,tf,i0,step_size
\ No newline at end of file
diff --git a/Part 1/midpoint.m b/Part 1/midpoint.m
index 7c3ed5c..9c8c180 100644
--- a/Part 1/midpoint.m
+++ b/Part 1/midpoint.m
@@ -1,8 +1,10 @@
 function [ x, y ] = midpoint( f, t0, tfinal, y0, h)

 

 N = round((tfinal - t0) / h);

-ya = zeros(1,N); ta = zeros(1,N);

-ya(1) = y0; ta(1) = t0;

+ya = zeros(1,N);

+ta = zeros(1,N);

+ya(1) = y0; 

+ta(1) = t0;

 

 for i = 1 : N - 1

     ta(i+1) = ta(i) + h;

diff --git a/Part 1/ralston.m b/Part 1/ralston.m
index 6041374..ac134c3 100644
--- a/Part 1/ralston.m
+++ b/Part 1/ralston.m
@@ -1,15 +1,18 @@
-function [t,vout] = ralston(func, t0, tf,i0 , h)

+function [xa,ya] = ralston(func, t0, tf,i0 , h)

 

-n = ((tf - t0) / h);

+N = round((tf) / h);

+xa = zeros(1,N);

+ya = zeros(1,N);

+xa(1)=t0;

+ya(1)=i0;

+

+%param

 a1=1/3;

 a2=2/3;

 p1=3/4;

 q11=3/4;

 

-xa(1)=t0;

-ya(1)=i0;

-

-for i=1:1:n

+for i=1: N - 1

     xtemp=xa(i);

     ytemp=ya(i); 

     

@@ -20,6 +23,3 @@ k2=func(xtemp+p1*h,ytemp+q11*k1*h);
 ya(i+1)=ytemp+(a1*k1+a2*k2)*h;

 xa(i+1)=xtemp+h;

 end

-

-t = xa;

-vout = ya;
\ No newline at end of file
diff --git a/Part 1/zihan_error.m b/Part 1/zihan_error.m
new file mode 100644
index 0000000..cbabc50
--- /dev/null
+++ b/Part 1/zihan_error.m
@@ -0,0 +1,37 @@
+clear;

+%inital

+ts = 0;     % set initial value of x_0

+is = 0;

+

+%parameter

+tf = 0.03;     % stop here

+R = 0.5;

+L = 0.0015; 

+

+

+

+%vin and the function

+A = 6;

+T = 0.00015;

+vin = @(t) A * cos(2*pi*t/T);

+func = @(t, iout) (vin(t) - iout*R) / L;      % define func

+

+

+for ind=3:16 % choose these carefully

+ h1=2^(-ind); % set stepsize

+ 

+    [t, iout, exact] = midpoint(func, ts, tf, is, h1);

+    

+    figure;

+    plot(exact)

+    

+%     vout = vin - R*iout;

+%     

+%     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

diff --git a/Part 1/zihan_error2.m b/Part 1/zihan_error2.m
new file mode 100644
index 0000000..5f9d643
--- /dev/null
+++ b/Part 1/zihan_error2.m
@@ -0,0 +1,40 @@
+%-----------------------------------------------------------------

+clear;

+ts = 0;     % set initial value of x_0

+is = 0;

+tf = 0.03;     % stop here

+R = 0.5;

+L = 0.00015;

+

+A = 6;

+T = 0.00015;

+

+vin = @(t) A * cos(2*pi*t/T);

+func = @(t, iout) (vin(t) - iout*R) / L;      % define func

+

+%obtaining the exact solution with favorite method

+

+%error as a function of t

+%error = exact - vout; 

+

+figure;

+

+for ind=16:50 % choose these carefully

+

+    h1=2^(-ind); % set stepsize

+    [t, i_Exact] = exact_solution(R,L,T,tf,h1);

+    exact = vin(t) - R*i_Exact;

+

+    [t, iout] = ralston(func, ts, tf, is, h1);

+    vout = vin(t) - R*iout;

+

+    error = exact - vout; 

+    error = max(abs(error));

+

+    plot(log(h1),log(error)); % log/log plot stepsize vs error

+    xlabel({'Step size', '(h)'});

+    ylabel({'Error'});

+    title('MIDPOINT');

+    hold on; % for next value to be plotted

+ 

+end