What is the most elegant way to get yp from solution of ODE15i?

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Tom Clark
Tom Clark 2015-5-13
评论： Tom Clark 2015-5-13
Hi,
I'm solving an ODE using ODE15i. As per the usual use case of 15i, the function I'm integrating is a function of t,y,and prime (the time derivative of y):
function sol = myFunc
% Set up ICs and shared variables
sol = ode15i(@nested_integrand,tspan,y0,yp0)
function f = nested_integrand(t,y,yp)
% some code
end
end
However, the solution sol only contains values of t and y at the integration points. Not yp! This seems like an oversight to me, since the consistent values of yp have already been calculated within ode15i.
So my question is in two parts:
1. What is the most elegant way of getting the yp values that correspond with sol.t and sol.y?
2. Does anyone else have a use for this output? If so I'll make a feature request.
Thanks all,
Tom

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采纳的回答

Torsten
Torsten 2015-5-13
[Y,YP] = deval(sol,tspan)
will give you the time-derivatives of your solution variables at times tspan in the matrix YP if your call to ode15i was
sol = ode15i(@nested_integrand,tspan,y0,yp0)
Best wishes
Torsten.
  1 个评论
Tom Clark
Tom Clark 2015-5-13
Perfect, thanks Torsten. I'd studied the documentation of deval() but my eyes must be swimming, as I'd missed that!
What a hero :)
Tom

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更多回答（1 个）

Torsten
Torsten 2015-5-13
If you solve for n unknowns y1,...,yn,
add n additional algebraic equations as
y(n+1)-dy(1)=0,y(n+2)-dy(2)=0,...,y(2*n)-dy(n)=0.
y(n+1),...,y(2*n) will then give you the derivatives of the variables you solved for.
Best wishes
Torsten.
  2 个评论
Tom Clark
Tom Clark 2015-5-13
Thanks Torsten, nice implementation. Would this affect the performance of the solver though?
Torsten
Torsten 2015-5-13
Maybe if n is large ...
But I think it's less time-consuming than to solve f(t,y,yp)=0 (with fsolve,e.g.) for each output time.
Best wishes
Torsten.

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