ODE 45 Extra parameter

Hello

I hope you're well.

I am currently trying to plot with ODE45. This is a linear growth model.

My formula is (r*p*(1-p/N)) - ((200/2)*(1+sin(2*pi*t)/12))

ODE45 works fine when solving with just the first part of the formula

sol = ode45(@(t,p) (r*p*(1-p/N)) , tspan, p0);

however I am not sure how to implement the extra bit of code. I tried the following

sol = ode45(@(t,p) (r*p*(1-p/N)) - ((200/2)*(1+sin(2*pi*t)/12)), tspan,p0);

But dont think this is correct.

I'm not sure how to implement this extra bit. Would appreciate any help.

Thanks.

Kind regards,

[Torsten]

If your ODE is

dp/dt = r*p*(1-p/N) - 200/2*(1+sin(2*pi*t)/12)

with p(0) = p0, your settings are correct.

[Steven Lord]

Is there something in particular that leads you to doubt the answer you receive when you run your code? If so can you show us your code and explain your doubt in more detail?

[See Goo]

Thank you for the responses.

I am asked to run only for 15 instances, which represent 15 years.

The first and second case look identical except for after the 15 years time frame where i see some sinusoidal activity.

%Q1

tspan = [0 15];

p0 = 1000 + 1000*2;

r = 0.25;

N =20000;

ode = ode45(@(t,p) r*p*(1-p/N), tspan,p0);

t = linspace(0,15);

devals = deval(ode,t);

plot(t,devals);

xlabel('t');

ylabel('p');

%Q2

tspan = [0 15];

p0 = 1000 + 1000*2;

r = 0.25;

N =20000;

ode = ode45(@(t,p) r*p*(1-p/N) - ((200/2)*(1+sin(2*pi*t)/12)), tspan,p0);

t = linspace(0,15);

devals = deval(ode,t);

plot(t,devals);

xlabel('t');

ylabel('p');

Answer 1

[Torsten]

I think there is quite a noticable difference between the solution curves.

%Q1
tspan = [0 15];
a = 1000 + 1000*2;
r = 0.25; 
N =20000;
options = odeset('RelTol',1e-12,'AbsTol',1e-12);
[t,ode] = ode45(@(t,p) r*p*(1-p/N), tspan,a,options);
plot(t,ode)
hold on
%t = linspace(0,15);
%devals = deval(ode,t);
%plot(t,devals);
%xlabel('t');
%ylabel('p');

%Q2
tspan = [0 15];
a = 1000 + 1000*2;
r = 0.25; 
N =20000;
[t,ode] = ode45(@(t,p) r*p*(1-p/N) - ((200/2)*(1+sin(2*pi*t)/12)), tspan,a,options);
plot(t,ode)
hold off
%t = linspace(0,15);
%devals = deval(ode,t);
%plot(t,devals);
xlabel('t');
ylabel('p');