How to find an approximate solution to a perturbed differential equation in Matlab?

Hi,

I need to be able to find an approximate solution using ode45 to a perturbed differential equation (specifically, x''-x=epsilon*t*x) where epsilon is much smaller than 1.

I understand how to use ode45 to solve the differential equation without the perturbation, but what does it mean to solve the Diff EQ with epsilon not equal to zero?

Thanks for any help!

Answer 1

[Mischa Kim]

Connie, the unperturbed differential equation is simply

 x'' - x = 0   % or should it rather say x'' + x = 0?

which you can solve analytically and by hand. For the perturbed case just look at the equation as a standard differential equation, which you solve, as you mentioned, using e.g. ode45.

 function pertODE()
 tspan   = 0:0.1:10;
 IC      = [1 1];
 epsilon = 0.05;

 [t,X] = ode45(@myODE,tspan,IC,[],epsilon);
 x     = X(:,1);
 v     = X(:,2);
 plot(t,x,'r')
 xlabel('t')
 ylabel('x')
 grid
 end

 function dY = myODE(t,y,epsilon)
 dY = zeros(2,1);
 x  = y(1);
 v  = y(2);
 dY = [ v;...
       -x + epsilon*t*x];
 end