Filter löschen
Filter löschen

Substitute partial differential into symfun

8 Ansichten (letzte 30 Tage)
ludolfusexe
ludolfusexe am 15 Mai 2024
Kommentiert: ludolfusexe am 16 Mai 2024
Because my actual functions are very complex, I would like to calculate the derivative of nested functions first and then substitute the functions afterwards.
A minimal example looks like this:
syms G(h) h(t) t
Q = G(h)
Q = 
dGdt = diff(Q,t) % -> D(G)(h(t)) occurs
dGdt = 
% Now define G(h) and derive:
G = h^2;
dGdh = diff(G,h)
dGdh(t) = 
How is it possible, to insert the derivative of G with respect to h as the partial derivative?
I tried this, but it is not working:
% dQ_subs = subs(dGdt, D(G), dGdh)
% dQ_subs = subs(dGdt, D(G)(h(t)), dGdh)
I really appreciate any feedback!

Akzeptierte Antwort

Torsten
Torsten am 15 Mai 2024
Verschoben: Torsten am 15 Mai 2024
syms G(h) h(t) t
Q = G(h)
Q = 
dGdt = diff(Q,t) % -> D(G)(h(t)) occurs
dGdt = 
s = children(dGdt)
s = 1x2 cell array
{[D(G)(h(t))]} {[diff(h(t), t)]}
% Now define G(h) and derive:
G = h^2;
dGdh = diff(G,h)
dGdh(t) = 
subs(dGdt,s{1},dGdh)
ans = 
  2 Kommentare
Paul
Paul am 15 Mai 2024
Bearbeitet: Paul am 15 Mai 2024
Hi Torsten,
I think it works easier, and perhaps more generally, to define G as a function of its own dummy variable.
syms G(x) h(t) t
Q = G(h);
dGdt = diff(Q,t) % -> D(G)(h(t)) occurs
dGdt = 
% Now define G(x) and derive:
G(x) = x^2;
subs(dGdt)
ans = 
Slightly more complicated case
G(x) = x^2 + sin(x);
subs(dGdt)
ans = 
ludolfusexe
ludolfusexe am 16 Mai 2024
Thank you very much for your two answers, both are very helpful.

Melden Sie sich an, um zu kommentieren.

Weitere Antworten (0)

Produkte


Version

R2022a

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by