Add files via upload

5 files changed, 311 insertions, 46 deletions

diff --git a/Part 1/error_script.m b/Part 1/error_script.m
new file mode 100644
index 0000000..43f8dda
--- /dev/null
+++ b/Part 1/error_script.m
@@ -0,0 +1,64 @@
+%-----------------------------------------------------------------

+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

+exact= @(t) 0.07553*cos( 41883.7*(t) ) + 0.94901*sin( 41883.7*(t) ); % works for arrays

+

+%error as a function of t

+error = @(t) exact(t) -vout; 

+

+figure(2);

+plot(t,error); %for midpoint

+loglog(error);

+

+%--------------------------------------------------------------------

+

+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 ] = ralston(func, ts, tf, is, h);

+

+%numerical solution

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

+

+%obtaining the exact solution with favorite method

+exact= @(t) 0.07553*cos( 41883.7*(t) ) + 0.94901*sin( 41884.7*(t) ); % works for arrays

+

+%error as a function of t

+error = @(t) exact(t) -vout; 

+

+figure(3);

+plot(t,error); %for ralston

+loglog(error);

+

+

+

+

+

+

diff --git a/Part 1/error_script_heun.m b/Part 1/error_script_heun.m
new file mode 100644
index 0000000..bb511bd
--- /dev/null
+++ b/Part 1/error_script_heun.m
@@ -0,0 +1,30 @@
+function error_script_heun (tf)

+

+ts = 0;     % set initial value of x_0

+is = 0;

+h = 0.0001;  % set step-size

+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 ] = heun(func, ts, is, h);

+

+%numerical solution

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

+

+%obtaining the exact solution with favorite method

+exact= @(t) 0.07553*cos( 41883.7*(t) ) + 0.94901*sin( 41883.7*(t) ); % works for arrays

+

+%error as a function of t

+error=exact-vout; 

+

+figure(1);

+plot(t,error); %for heun

+loglog(error);

+

+end
\ No newline at end of file
diff --git a/Part 1/heun_script.m b/Part 1/heun_script.m
index 264942f..fdf9a62 100644
--- a/Part 1/heun_script.m
+++ b/Part 1/heun_script.m
@@ -42,18 +42,9 @@ title('(Heaviside) V_{out} versus time');
 

 %---------------------------------------------------------------------------------------------

 

-%initailise the circuits 

-R = 0.5;

-L = 1.5*10^(-3);

-h = 0.00001; %step size

-

-

-%initailise the container 

+%initailise the circuits at the top

 

-N = round(tf/h); %number of iterations

-t = zeros(1, N);

-Vout = zeros(1, N);

-current = zeros(1,N);

+%initailise the container at the top

 

 %input voltage

 tau = 0.000150;

@@ -86,18 +77,9 @@ title('(Exponential #1) V_{out} versus time');
 

 %-----------------------------------------------------------------------------------------------

 

-%initailise the circuits 

-R = 0.5;

-L = 1.5*10^(-3);

-h = 0.00001; %step size

+%initailise the circuits at the top

 

-

-%initailise the container 

-

-N = round(tf/h); %number of iterations

-t = zeros(1, N);

-Vout = zeros(1, N);

-current = zeros(1,N);

+%initailise the container at the top

 

 %input voltage

 tau = 0.000150;

@@ -132,13 +114,10 @@ title('#(Exponential #2) V_{out} versus time');
 %-------------------------------------------------------------------------------------------

 

 

-%initailise the circuits 

-R = 0.5;

-L = 1.5*10^(-3);

-h = 0.00001; %step size

+%initailise the circuits at the top

 

 

-%initailise the container 

+%initailise the container at the top

 

 N = round(tf/h); %number of iterations

 t = zeros(1, N);

@@ -174,18 +153,11 @@ title('(Sine wave) V_{out} versus time ');
 

 %-----------------------------------------------------------------------------------------

 

-%initailise the circuits 

-R = 0.5;

-L = 1.5*10^(-3);

-h = 0.00001; %step size

+%initailise the circuits at the top

 

 

 %initailise the container 

 

-N = round(tf/h); %number of iterations

-t = zeros(1, N);

-Vout = zeros(1, N);

-current = zeros(1,N);

 

 %input voltage

 % step function of 5 volt

@@ -218,18 +190,9 @@ ylabel({'V_{out}', '(volt)'});
 title('(Square wave) V_{out} versus time');

 

 %--------------------------------------------------------------------------------------

-%initailise the circuits 

-R = 0.5;

-L = 1.5*10^(-3);

-h = 0.00001; %step size

-

+%initailise the circuits at the top

 

-%initailise the container 

-

-N = round(tf/h); %number of iterations

-t = zeros(1, N);

-Vout = zeros(1, N);

-current = zeros(1,N);

+%initailise the container at the top

 

 %input voltage

 % step function of 5 volt

diff --git a/Part 1/midpoint_script.m b/Part 1/midpoint_script.m
new file mode 100644
index 0000000..35ace43
--- /dev/null
+++ b/Part 1/midpoint_script.m
@@ -0,0 +1,104 @@
+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;

+

+vin = @(t) 3.5;

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

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

+

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

+plot(t,vout);

+xlabel({'Time', '(seconds)'});

+ylabel({'V_{out}', '(volt)'});

+title('V_{out} versus time (original function)');

+%____________________________________________________________________

+h = 0.0001;

+tf = 0.03;

+figure;

+A = 3.5;

+tau = 0.000150;

+

+vin = @(t) A * exp(-t.^2/tau);

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

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

+

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

+plot(t,vout);

+xlabel({'Time', '(seconds)'});

+ylabel({'V_{out}', '(volt)'});

+title('V_{out} versus time (exponential square funtion)');

+%____________________________________________________________________

+h = 0.0001;

+tf = 0.03;

+figure;

+A = 3.5;

+tau = 0.000150;

+

+vin = @(t) A * exp(-t/tau);

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

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

+

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

+plot(t,vout);

+xlabel({'Time', '(seconds)'});

+ylabel({'V_{out}', '(volt)'});

+title('V_{out} versus time (exponential function)');

+

+%____________________________________________________________________

+h = 0.0001;

+tf = 0.03;

+figure;

+A = 4;

+T = 0.0015;

+

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

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

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

+

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

+plot(t,vout);

+xlabel({'Time', '(seconds)'});

+ylabel({'V_{out}', '(volt)'});

+title('V_{out} versus time (sine function)');

+%____________________________________________________________________

+h = 0.0001;

+tf = 0.03;

+figure;

+A = 4;

+T = 0.0015;

+

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

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

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

+

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

+plot(t,vout);

+xlabel({'Time', '(seconds)'});

+ylabel({'V_{out}', '(volt)'});

+title('V_{out} versus time (square function)');

+%____________________________________________________________________

+h = 0.0001;

+tf = 0.03;

+figure;

+A = 4;

+T = 0.0015;

+

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

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

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

+

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

+plot(t,vout);

+xlabel({'Time', '(seconds)'});

+ylabel({'V_{out}', '(volt)'});

+title('V_{out} versus time (sawtooth function)');

+

+

+

+

+

+

diff --git a/Part 1/ralston_script.m b/Part 1/ralston_script.m
new file mode 100644
index 0000000..91da2a9
--- /dev/null
+++ b/Part 1/ralston_script.m
@@ -0,0 +1,104 @@
+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;

+

+vin = @(t) 3.5;

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

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

+

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

+plot(t,vout);

+xlabel({'Time', '(seconds)'});

+ylabel({'V_{out}', '(volt)'});

+title('V_{out} versus time (original function)');

+%____________________________________________________________________

+h = 0.0001;

+tf = 0.03;

+figure;

+A = 3.5;

+tau = 0.000150;

+

+vin = @(t) A * exp(-t.^2/tau);

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

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

+

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

+plot(t,vout);

+xlabel({'Time', '(seconds)'});

+ylabel({'V_{out}', '(volt)'});

+title('V_{out} versus time (exponential square funtion)');

+%____________________________________________________________________

+h = 0.0001;

+tf = 0.03;

+figure;

+A = 3.5;

+tau = 0.000150;

+

+vin = @(t) A * exp(-t/tau);

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

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

+

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

+plot(t,vout);

+xlabel({'Time', '(seconds)'});

+ylabel({'V_{out}', '(volt)'});

+title('V_{out} versus time (exponential function)');

+

+%____________________________________________________________________

+h = 0.0001;

+tf = 0.03;

+figure;

+A = 4;

+T = 0.0015;

+

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

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

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

+

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

+plot(t,vout);

+xlabel({'Time', '(seconds)'});

+ylabel({'V_{out}', '(volt)'});

+title('V_{out} versus time (sine function)');

+%____________________________________________________________________

+h = 0.0001;

+tf = 0.03;

+figure;

+A = 4;

+T = 0.0015;

+

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

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

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

+

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

+plot(t,vout);

+xlabel({'Time', '(seconds)'});

+ylabel({'V_{out}', '(volt)'});

+title('V_{out} versus time (square function)');

+%____________________________________________________________________

+h = 0.0001;

+tf = 0.03;

+figure;

+A = 4;

+T = 0.0015;

+

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

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

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

+

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

+plot(t,vout);

+xlabel({'Time', '(seconds)'});

+ylabel({'V_{out}', '(volt)'});

+title('V_{out} versus time (sawtooth function)');

+

+

+

+

+

+