Using the euler method

Hi something is wrong with my for loop i have no idea what to do

% write a program that will explore population dynamics
% The population dynamics of a community can be described by:
% dp/dt = G(Pmax - P(t))*P(t)
% Use Euler's Method to determine the population (") as a function of time (#)
% Plot the population (") as a function of time (#) from t = 0 to t = 20 years
% Use the following values for constants in the differential equation:
% pmax = 10,000
% G = 0.00005
% Use an initial condition of p = 800 when t=0 
%% set perameters
pmax = 10000 
G = 0.00005 
tmin = 0
tmax = 20
Nx = 50
t = linspace(tmin, tmax, Nx)
dt = t(1)-t(0)
p = zeros(1,Nx)
p(0) = 800
%% calculate p values using euler method
p(1) = G*(pmax - p(0))*p(0)*dt+p(0)
for ip = 1:Nx
    p(ip+1) = G*(pmax - p(t(ip))*p(t(ip))*dt+p(t(ip))
end

Answer 1

[Geoff Hayes]

Kelsey - there are a couple of coding mistakes with the above. Before the code can execute, there is an error

Invalid expression. When calling a function or indexing a variable, use parentheses. Otherwise, check for
mismatched delimiters.

with the line

p(ip+1) = G*(pmax - p(t(ip))*p(t(ip))*dt+p(t(ip))

becaue there is a missing closing bracket. The above line should be

p(ip+1) = G*(pmax - p(t(ip))*p(t(ip))*dt+p(t(ip)));

Next, there is the error

Array indices must be positive integers or logical values.

with the line

dt = t(1)-t(0)

As the error message indicates, positive integers or logical values must be used as indices. 0 is not a positive integer, so you if you want to find the delta, then just do

dt = t(2)-t(1)

Similarly, you must change

p(0) = 800
%% calculate p values using euler method
p(1) = G*(pmax - p(0))*p(0)*dt+p(0)
for ip = 1:Nx

to

p(1) = 800
%% calculate p values using euler method
p(2) = G*(pmax - p(1))*p(1)*dt+p(1)
for ip = 2:Nx

The final problem will be with

p(ip+1) = G*(pmax - p(t(ip))*p(t(ip))*dt+p(t(ip)));

and the error

Array indices must be positive integers or logical values.

because of p(t(ip)) where you are using the vaues of t - which are not integers - as indices into p. What is this code trying to do here?

[Kelsey Pettrone]

just to take the formula that was given and use eulers method and a for loop to find the population from 1 to 20 years

Answer 2

[James Tursa]

p(ip) is the value of p at time t(ip). p isn't a function that you are passing time into like you are doing with p(t(ip)). So get rid of that t(ip) subscripting and simply use ip subscripting instead. E.g.,

p(ip+1) = G*(pmax - p(ip))*p(ip)*dt + p(ip);

Also, the initial condition is p = 800, and the initial value is p(1), so replace that p(1) line with simply

p(1) = 800;

and get rid of the p(0) = 800 line since 0 is not a valid subscript.

Which also means that the dt calculation should be this:

dt = t(2) - t(1);

[Kelsey Pettrone]

then should my for loop go from 1 to 20 instead?

[James Tursa]

No. Keep your for-loop running from 1 to Nx since that is what matches the dt you created. The time is still running from 0 to 20 because of how you have built the t array. E.g., you could increase Nx to 100 or 500 and things would still be OK for using Nx in the for-loop because the dt value would decrease. Time would still be running from 0 to 20.

[Kelsey Pettrone]

and i think it might be this

p(ip) = G*(pmax - p(ip-1))*p(ip-1)*dt + p(ip-1);

with -1 but im not sure

would this make sense?

[James Tursa]

This depends on how you do the for-loop indexing. If the for-loop index starts at 1, then you use ip+1 on the lhs and ip on the rhs. If the for-loop index starts at 2, then you would use ip on the lhs and ip-1 on the rhs. Either way works ... personal preference.