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Question: Analytic derivatives of numerical solutions of an ODE system

Question:Analytic derivatives of numerical solutions of an ODE system

apdstb 28 Maple
derivative ode dsolve numeric differential-equations
October 18 2007
0
Hello!

I have a system of ODEs which I can solve numericaly with Maple. What I try to do (still without success) is to compute the i-th derivatives of the solutions at a certain point of the interval. For example (a mini-version):

eq_0 := D(x[0])(t)=(-2*x[0](t))/(1-x[1](t));
eq_1 := D(x[1])(t)=(2*x[0](t))/(1-x[1](t));
sys := {eq_0, eq_1, x[0](0)=1, x[1](0)=0};
fcns := {x[0](t), x[1](t)};
p:=dsolve( sys, fcns, numeric, method=classical[rk2], output=listprocedure );

(OK, this is very easy, but it is only an example.)

Now I want to compute the 6-th derivative of x[0](t) at t=1/2. The analytic form can be obtained if D(x[0]) is differentiated 5 times and x[0] and x[1] are substituted by their numerical solution. I have read about differantiating in Maple, but I still cannot get this work.

Many thanks for any help

Alexandros
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