How to plot same function from different starting positions

So I want to plot a function of temperature over time, however I want to see how the temperature changes when it's at different starting points going from 0 to 28 going in steps of 2.

Is there a simple way to change the starting point and have it all plot on the same graph without having to rewrite the function out multiple times?

This is the code:

C = 51
absorbed_solar_radiation = 239.4 ;
A = 221.2 ;
B = -1.3 ;
greenhouse_effect_PI = 0

dt = 1 ;

T0 = 5 ; %This is the starting temperature I want to change
T(1) = T0 ;

t0 = 0 ;
t(1) = t0 ;

n_step = 200 ;

for n = 1:n_step ;
    t(n+1) = t(n) + dt;
    T(n+1) = T(n) + (dt/C)*(absorbed_solar_radiation - (A - B*T(n)) + greenhouse_effect_PI) ;
end


plot(t,T, 'b.-')
xlabel('years')
ylabel('temperature')

The temperature should always tend to 14. So my question is, is there a neat way to change 'T0' without having to list all the starting points as different variables and have to write out:

T(n) + (dt/C)*(absorbed_solar_radiation - (A - B*T(n)) + greenhouse_effect_PI) ;

multiple times?

Answer 1

[KSSV]

C = 51 ;
absorbed_solar_radiation = 239.4 ;
A = 221.2 ;
B = -1.3 ;
greenhouse_effect_PI = 0 ;

dt = 1 ;
n_step = 200 ;

T0 = 5:2:20 ; % possile values of T0 
m = length(T0) ;   % length of T0 
T = zeros(m,n_step) ;  % initialize the required data 

t0 = 0 ;
t = t0:dt:n_step-1 ;    % time step 
for i = 1:m  % loop for each T 
    T(i,1) = T0(i) ;   % pick the initial value 
    for n = 1:n_step-1     
        % calculate T and store in the data  
        T(i,n+1) = T(i,n) + (dt/C)*(absorbed_solar_radiation - (A - B*T(i,n)) + greenhouse_effect_PI) ;
    end
end

plot(t,T)
xlabel('years')
ylabel('temperature')
legend(num2str(T0'))

●

Answer 2

[Cai Beacham]

Thank you so much!

I understand that you've made T an 'm' by 'n_step' matrix of zeros but would it be possible for you to explain what you've done here:

for i = 1:m
    T(i,1) = T0(i) ;

And here:

    for n = 1:n_step ;
        T(i,n+1) = T(i,n) + (dt/C)*(absorbed_solar_radiation - (A - B*T(i,n)) + greenhouse_effect_PI) ;

Again, many thanks!

[KSSV]

I have commented in the code.