Message Boards Message Boards

GROUPS:

Find error in "NDsolve"

Posted 5 months ago
745 Views
|
4 Replies
|
3 Total Likes
|

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,

4 Replies

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?

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,

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.

Posted 5 months ago

Also works fine on 12.1.0 for Mac OS X x86 (64-bit) (March 14, 2020)

enter image description here

Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Reply Preview
Attachments
Remove
or Discard

Group Abstract Group Abstract