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

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Tom Clark 2015-5-13

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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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Answer 1

Torsten 2015-5-13

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[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.

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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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Answer 2

Torsten 2015-5-13

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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.

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Tom Clark 2015-5-13

Thanks Torsten, nice implementation. Would this affect the performance of the solver though?

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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