Hello, please I tried to solve this system by NDSolve, but I find errors and I do not know why!
if someone can help me?
Thank you
t1 = 2;
(Définit la fonction indicatrice)
indicator[x_] := Piecewise[{{1, 0 < x < 1/2}}, 0];
E1 = D[g[x, t], {x, 2}] - D[g[x, t], {t, 2}] == indicator[x]*((Cos[\[Pi] t1] - Sin[\[Pi] t1]) Sin[\[Pi] x])/(
4 \[Pi])*DiracDelta[t - t1];
ic = {g[x, 0] == Sum[Sin[k *\[Pi]*x], {k, 1}], Derivative[0, 1][g][x, 0] == Sum[k *\[Pi] *Sin[k *\[Pi]* x], {k, 1}]};
(*Condition aux bord de Dirichlet*)
bcc = {g[0, t] == 0, g[1, t] == 0};
(*résolution numérique de l'équation*)
sol11 = NDSolve[{E1, ic, bcc}, g, {x, 0, 1}, {t, 0, 12}, MaxStepSize -> 0.1];
Best regards,
hdolhaine
(Hans Dolhaine)
2
On my (old) system (Mathematica 7) your code runs without any error message and gives back in sol11 an InterpolatingFunction object. You can plot it
gF = g /. sol11[[1, 1]]
Plot3D[gF[x, y], {x, 0, 1}, {y, 0, 10}]
So, which errors do you find?
Also works fine on 12.1.0 for Mac OS X x86 (64-bit) (March 14, 2020)
Hey, sir, that’s exactly what I need.
gF = g /. sol11[[1, 1]]
I’m always having this problem extracting the solution, can you tell me please where I can find out more about this kind of order?
Best regards,
hdolhaine
(Hans Dolhaine)
5
Well, hmmm. Run your code and look at
sol11
(without semicolon)
Then you see that sol11 is a list of list.
You can extract the content with
sol11[[1,1]]
in the Help - section of your Mathematica you might want to look up Part.
The last command gives you a Rule (look that up as well)
it says g → something.
Now when you write
g/.sol11[[1,1]]
that rule is applied and g is substituted by the right hand side of the arrow ( look up ReplaceAll)
gF = g/.sol11[[1,1]]
assigns the InterpolatingFunction (the result of NDSolve) to the symbol gF, and then you can use gF in further operations.
I hope this helps a bit.
