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Question: Is it possible differentiation of a numerical solution ?

Question:Is it possible differentiation of a numerical solution ?

student_1 305
December 12 2018
2

Suppose that we want to solve second order a PDE by separation of variables method.

Let solution is Summation(X(x).T(t)),

Let X(x):= nPix/l;

And we want to find T(t) by numerical methods. After finding T(t) by numerical methods,

How to differentiate to Summation(X(x).T(t)) with respect to t?   

Briefly; I mean that

How to find derivative of u(t) after finding numerically as follows?

 

restart:
ode:=diff(u(t),t,t)+diff(u(t),t)-6*u(t)=0:
ICs:=u(0)=1,D(u)(0)=0:
dsolve({ode,ICs},numeric);
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