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function heun_script (tf) %tf is the end time
%initailise the circuits
R = 0.5;
L = 1.5*10^(-3);
h = 0.00001; %step size
%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
Vin = @(t)3.5*heaviside(t);
%the initial condition
t(1) = 0;
current(1) = 0;
%the equation
func = @(t,current) (Vin(t)-R*(current))/L; %Function input for difference method
%Huen
for j = 1 : N-1
[t(j + 1),current(j + 1)] = heun(func, t(j), current(j), h);
Vout(j + 1) = Vin(t(j)) - R*current(j); %Create Vout array from Iout, R and Vin
end
%plot
figure(1);
plot(Vout);
xlabel({'Time', '(seconds)'});
ylabel({'V_{out}', '(volt)'});
title('(Heaviside) V_{out} versus time');
%---------------------------------------------------------------------------------------------
%initailise the circuits at the top
%initailise the container at the top
%input voltage
tau = 0.000150;
A = 3.5;
Vin = @(t) A * exp(-t.^2/tau);
%the initial condition
t(1) = 0;
current(1) = 0;
%the equation
func = @(t,current) (Vin(t)-R*(current))/L; %Function input for difference method
%Huen
for j = 1 : N-1
[t(j + 1),current(j + 1)] = heun(func, t(j), current(j), h);
Vout(j + 1) = Vin(t(j)) - R*current(j); %Create Vout array from Iout, R and Vin
end
%plot
figure(2);
plot(Vout);
xlabel({'Time', '(seconds)'});
ylabel({'V_{out}', '(volt)'});
title('(Exponential #1) V_{out} versus time');
%-----------------------------------------------------------------------------------------------
%initailise the circuits at the top
%initailise the container at the top
%input voltage
tau = 0.000150;
A = 3.5;
Vin = @(t) A * exp(-t/tau);
%the initial condition
t(1) = 0;
current(1) = 0;
%the equation
func = @(t,current) (Vin(t)-R*(current))/L; %Function input for difference method
%Huen
for j = 1 : N-1
[t(j + 1),current(j + 1)] = heun(func, t(j), current(j), h);
Vout(j + 1) = Vin(t(j)) - R*current(j); %Create Vout array from Iout, R and Vin
end
%plot
figure(3);
plot(Vout);
xlabel({'Time', '(seconds)'});
ylabel({'V_{out}', '(volt)'});
title('#(Exponential #2) V_{out} versus time');
%-------------------------------------------------------------------------------------------
%initailise the circuits at the top
%initailise the container at the top
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
Vin = @(t)4*sin(2*pi*6000*t);
%the initial condition
t(1) = 0;
current(1) = 0;
%the equation
func = @(t,current) (Vin(t)-R*(current))/L; %Function input for difference method
%Huen
for j = 1 : N-1
[t(j + 1),current(j + 1)] = heun(func, t(j), current(j), h);
Vout(j + 1) = Vin(t(j)) - R*current(j); %Create Vout array from Iout, R and Vin
end
%plot
figure(4);
plot(Vout);
xlabel({'Time', '(seconds)'});
ylabel({'V_{out}', '(volt)'});
title('(Sine wave) V_{out} versus time ');
%-----------------------------------------------------------------------------------------
%initailise the circuits at the top
%initailise the container
%input voltage
% step function of 5 volt
A = 4;
T = 0.0015;
Vin = @(t) A * square(2*pi*t/T);
%the initial condition
t(1) = 0;
current(1) = 0;
%the equation
func = @(t,current) (Vin(t)-R*(current))/L; %Function input for difference method
%Huen
for j = 1 : N-1
[t(j + 1),current(j + 1)] = heun(func, t(j), current(j), h);
Vout(j + 1) = Vin(t(j)) - R*current(j); %Create Vout array from Iout, R and Vin
end
%plot
figure(5);
plot(Vout);
xlabel({'Time', '(seconds)'});
ylabel({'V_{out}', '(volt)'});
title('(Square wave) V_{out} versus time');
%--------------------------------------------------------------------------------------
%initailise the circuits at the top
%initailise the container at the top
%input voltage
% step function of 5 volt
A = 4;
T = 0.0015;
Vin = @(t) A * sawtooth(2*pi*t/T);
%the initial condition
t(1) = 0;
current(1) = 0;
%the equation
func = @(t,current) (Vin(t)-R*(current))/L; %Function input for difference method
%Huen
for j = 1 : N-1
[t(j + 1),current(j + 1)] = heun(func, t(j), current(j), h);
Vout(j + 1) = Vin(t(j)) - R*current(j); %Create Vout array from Iout, R and Vin
end
%plot
figure(6);
plot(Vout);
xlabel({'Time', '(seconds)'});
ylabel({'V_{out}', '(volt)'});
title('(Sawtooth wave) V_{out} versus time');
end
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