Piecewise, Evaluate, and NDSolve

Questions
,
1

Hi,
I solved an equation and the answer is the list of pieces

 For[j=1,j<=3,j++,
 {
  solution=NDSolve[
    {eq1, u[x,0]=? =(ampl[[j]]/Sqrt[2*Pi]/sigma[[j]])*Exp[-((x-ex[[j]])^2)/2/sigma[[j]]^2]} , u, {t,0,100}, {x,-100,100}
    ],
 
  pieceSolution[a_,b_]=Piecewise[{{0, b<time[[j]]},{Evaluate[u[a,b-time[[j]]]/.solution], b>=time[[j]]}}],
 
  temp[c_,d_]=sumSolution[c,d]+pieceSolution[c,d],
  sumSolution[c_,d_]=temp[c,d]
  }
 ]

sumSolution[a,b] (*In*)
(*Out*)({
   {\[Piecewise], {
     {0, b<1},
     {{InterpolatingFunction[{{-100.,100.},{0.,100.}},<>][a,-1+b]}, b>=1},
     {0, True}
    }}
  })+({
   {\[Piecewise], {
     {0, b<2},
     {{InterpolatingFunction[{{-100.,100.},{0.,100.}},<>][a,-2+b]}, b>=2},
     {0, True}
    }}
  })+({
   {\[Piecewise], {
     {0, b<5},
     {{InterpolatingFunction[{{-100.,100.},{0.,100.}},<>][a,-5+b]}, b>=5},
     {0, True}
    }}
  })

I can evaluate an equation in each single point:

(*In*) Evaluate[sumSolution[1,3]][[1]]
(*Out*)0.371703

(*In*)sumSolution[1,4]
(*Out*){0.300161}

But I can’t use NDSolve with Evaluate

xSol1=NDSolve[{D[r[v],v,v] = = ?Evaluate[sumSolution[r[v],v]][[1]],r[0]?= =0,r'[0]= =?0},r,{v,0,50}]
NDSolve::ndfdmc: Computed derivatives do not have dimensionality consistent with the initial conditions. ?
NDSolve[{r''[v]?({
{\[Piecewise], {
{0, v<0},
{{InterpolatingFunction[{{-100.,100.},{0.,100.}},<>][r[v],v]}, v>=0},
{0, True}
}}
}),r[0]?= =0,r'[0]= =?0},r,{v,0,50}]

What’s the deal and how can I fight it??

If sumSolution is just an InterpolationFunction, not “Piecewise construction” NDSolve works perfectly.

2

Some of your code might not have transmitted well. What are "r\[0]?0,r'\[0]?0" and “r¢¢”?

``

3

Sorry, I don’t have Mathematica installed on my network computer…It means r[0]= =0, r’[0]= =0; r’’ respectively. Corrected the code

4

Essentially I need to shift the solution u[x,t] to be equal to 0 if t<time[] and to evolve according to eq1 when t>=time[] with the initial condition of u[x,time[]]=? =(ampl[]/Sqrt[2*Pi]/sigma[])*Exp[-((x-ex[])^2)/2/sigma[]^2]}

5

Once again (it’s a printscreen)

1.png
1.png1152Ă—780 5.97 KB

2_OP_1_CP_.png
2_OP_1_CP_.png1152Ă—648 7.58 KB

It’s clear that Out[93]-Out[96] are lists.

3.png
3.png1152Ă—648 6.73 KB

But Out[97]-[99] are numbers.

Then I need to solve the motion equation where the right side is sumSolution[x,t].
Neither method evaluated sumSolution as a number

4.png
4.png1152Ă—648 7.8 KB

6

You would probably get better feedback when posting code that can be evaluated instead of a screenshot, but try something like

sS[c_?NumericQ, d_?NumericQ] := First[sumSolution[c, d]]; 
NDSolve[{x''[t] == sS[x[t], t], x[0] == 0, x'[0] == 0}, x, {t, 0, 100}]
7

I cant cause I dont have Mathematica installed on my network computer.
Thanks a lot for your help, it works!