Solving non homogenous differential equations numerically using ode45 etc

How is a non homogenous differential equation solved in MATLAB using ode45 or ode23. I have a function like:- dmdt = a*exp(Asin(wt) + (2-m)^2);

Can I obtain the numerical solution for this?

Thanks in advance

Answer 1

[Mischa Kim]

Sarah, yes you can. The typical approach for such an example is to create two functions:

 function my_EOM()
 a     = 1;
 A     = 1;
 w     = 1;
 fun   = @(w,x) sin(w.*x);
 param = {a; A; w; fun};

 IC    = -1;
 [t,m] = ode45(@EOM,[0 1],IC,[],param);

 plot(t,m)
 xlabel('t')
 ylabel('m')
 grid
 end

 function dmdt = EOM(t, m, param)
 a   = param{1};
 A   = param{2};
 w   = param{3};
 fun = param{4};

 dmdt = a*exp(A*fun(w,t) + (2 - m)^2);
 end

Save both functions in the same .m-file and with name my_EOM.m. Execute and enjoy.

[Sarah Ghosh]

Thanks for your answer, but is there no possible way to pass the external input to the ode function (here, EOM). I basically want to plot and check the external input and the solution obtained via the differential equation. So, I need the external input in the my_EOM function so that I have both these two as vectors. Is there any way to do that? Or do I just create the input again in my_EOM?

[Mischa Kim]

See updated answer.

Answer 2

[Orion]

you can rewrite your equation as :

dmdt + a*exp(Asin(wt)) * exp((2-m)^2) = 0

which is of the form of

y'(t) + f(t)y(t) = g(t)

with

y'(t) = dmdt

f(t) = a*exp(Asin(wt))

y(t) = exp((2-m)^2)

g(t) = 0

This is similar to the example 3 of the page ode45

Look how it is resolved and just adapt it to your problem.