Re: lsode twice problem

[Montgomery-Smith, Stephen]

On 01/17/2014 02:17 PM, marciopfrs wrote:
> Hello,
> 
> I'm using the following commands to solve the ODE:
> %         y''(t) = (y'(t))^2/2 - 2y +2
> %         y(0) = 1?
> %         y'(0) = 0?
> % using the system 
> % Y(1) = v'= v^2/2 - 2y +2
> % Y(2) = y' = v
> % X(1) = v
> % X(2) = y
> function Y=f(X,t); Y=[X(1)*X(1)/2 - 2*X(2) + 2, X(1)]'; endfunction;
>       X0 = [.7, .845]';
>       t = linspace(0, 20, 91);
>       X = lsode('f', X0, t);
> %     plot(t, X(:,1), t, X(:,2))
> %     plot(t, X(:,2))
> 
> I tried a lot but was not able to use the solution "y" of this ODE in
> another ODE
> %w'=y*w +1.
> 
> How can I do this?

To answer Robert Durkacz's point, here is a different way.

% Wp = w'
% W = w

global pp
pp = spline(t,X(:,2));
function Wp=g(W,t); global pp; Wp = ppval(pp,t)*W(1) + 1; endfunction
W = lsode('g',0,t);
plot(t,W)