lsode diverges for large coefficients?

[Olaf Till]

Sorry, I lost the original mail and cannot reply directly.

> The ODE solver lsode seems to diverge for large values of k in
> equations of the form
> 
> x'' = kx
> 
> even when the initial conditions are specified such that the solution
> is a constant (eg x(0) = 100 and x'(0) = 0).
> 

These initial conditions can not give a constant solution, use [0; 0]
for that. lsode does not produce constant solutions in _both_ cases
below, maybe you have mistaken the first solution for constant due to
setting the y axis range in the plot --- look at the raw values after
"format long".

> 
> Repeat-By:
> ---------
> 
> % 4/1/2009 Jim Bridgewater (jwbwater at gmail.com)
> % Octave bug report
> 
> % Keep octave from complaining about function statement at the
> % beginning of a script file
> dummy = 5; 
> 
> % setup the differential equations to produce correct output
> % c'' = 1e3 * c
> function cdot = f(c, x)
>   A = [0 1e3; 1 0];
>   B = [0 0]';
>   cdot = A * c + B;
> endfunction
> 
> % setup the differential equations to reproduce bug
> % c'' = 1e9 * c
> function cdot = g(c, x)
>   A = [0 1e9; 1 0];
>   B = [0 0]';
>   cdot = A*c + B;
> endfunction
> 
> x = linspace (0, 2e-5, 30);
> c0 = [0 100]';
> 
> y1 = lsode ("f", c0, x);
> y2 = lsode ("g", c0, x);
> subplot(2,1,1)
> plot(x,y1(:,2))
> axis([0 x(end) 99.9 100.1])
> subplot(2,1,2)
> plot(x,y2(:,2))