How to solve two differential equations using ode45.
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Ebraheem Menda
le 22 Fév 2018
Commenté : Ebraheem Menda
le 1 Juil 2021
My system is this
x"+ x'+ x + y'=0;
y"+ y'+ y + x'=0;
i need to solve these differential equations using ode's.
thanks in advance.
2 commentaires
Torsten
le 22 Fév 2018
You will need four initial conditions (for x,x',y,y') if you want to use ODE45 as numerical solver.
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Torsten
le 22 Fév 2018
fun=@(t,y)[y(2);-y(2)-y(1)-y(4);y(4);-y(4)-y(3)-y(2)];
x0=...; %supply x(t0)
x0prime=...; %supply x'(t0)
y0=...; %supply y(t0)
y0prime=...; %supply y'(t0)
Y0=[x0; x0prime; y0; y0prime];
tspan=[0 5];
[T,Y]=ode45(fun,tspan,Y0);
plot(T,Y(:,1)) %plot x
plot(T,Y(:,3)) %plot y
Best wishes
Torsten.
9 commentaires
Andreas Zimmermann
le 16 Avr 2020
Modifié(e) : Andreas Zimmermann
le 16 Avr 2020
Hi Joe,
Using Torsten's relations
x = y(1)
x' = y(2)
y = y(3)
y' = y(4)
the first line
fun=@(t,y)[y(2); -y(2)-y(1)-y(4); y(4); -y(4)-y(3)-y(2)];
can be translated to the following, using Torsten's relations:
[x'; -x'-x-y'; y'; -y'-y-x']
which is essentially
[x'; x"; y'; y"].
He got these relations by solving for x" and y":
x"+ x'+ x + y'=0; => x" = -x' -x -y' = -y(2) -y(1) -y(4)
y"+ y'+ y + x'=0; => y" = -y' -y +x' = -y(4) -y(3) -y(2)
I have tried to use ode45 to solve the SIR model from this fantastic Geogebra Tutorial: (https://youtu.be/k6nLfCbAzgo)
% Just some start parameters and coefficients
Istart = 0.01;
Sstart = 0.99;
Rstart = 0;
transm = 3.2;
recov = 0.23;
maxT = 20;
% define S',I',R'
% S' = - transm * S * I
% I' = transm * S I - recov * I
% R' = recov * I
% S is y(1)
% I is y(2)
% R is y(3)
%so here fun = @(t,y)[S'; I'; R'];
fun = @(t,y)[-transm*y(1)*y(2); (transm*y(1)*y(2))-(recov*y(2)); recov*y(2)];
% Provide the starting parameters
Y0 = [Sstart; Istart; Rstart;];
% Define the range of t
tspan = [0 maxT];
% Magic happens and matrix Y contains S,I,R
[T,Y] = ode45(fun,tspan,Y0);
% Plot plot
figure
plot(T,abs(Y(:,1)),'b-') % S
hold on
plot(T,abs(Y(:,2)),'r-') % I
plot(T,abs(Y(:,3)),'g-') % R
xlim([0 23])
%Hope this helps :)
% Many thanks to Torsten and Ebraheem for your very very useful discussion!
Plus de réponses (3)
Abraham Boayue
le 24 Fév 2018
Hey Ebraheem There are many excellent methods that you can use to solve your problem, for instance, the finite difference method is a very powerful method to use. I can try with that.The ode45 function is a matlab built in function and was designed to solve certain ode problems, it may not be suitable for a number of problems. What are the initial values of your equations? Do you have any plot of the solution that one can use as a guide?
Abraham Boayue
le 24 Fév 2018
The finite difference method is used to solve differential and partial equations. It is easier to implement in matlab. You can do the coding in any version of matlab, I have taken a course in numerical mathematics before and have a fairly good knowledge of how to solve such problems.
5 commentaires
Abraham Boayue
le 19 Juil 2020
Hi Ebraheem Is there anything specific that you want me to do for you?
2 commentaires
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