## 28 Reputation

17 years, 111 days

## Analytic derivatives of numerical soluti...

Maple
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.

## plotting functions of solutions of an OD...

Maple
Hello!

I use Maple 9 for some weeks and it helps me a lot. In the last days I have 2 problems that I could not implement in Maple. I spent many hours reading manuals, tips etc. without finding an idea, so I decided to post here my questions:

I use dsolve (numeric) to solve a system of ODEs. I receive the solution "p" wich I can plot whithout problems.

Question 1
----------

After this, I define a new function "S" as:

S := t -> p(t)[2] + p(t)[3] + p(t)[4] + p(t)[5];

I tried to plot it with

e:=1.5;
interface(plotoutput="sum.ps");
plot(S, 1..e);