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My code involves integrating the a function, which requires the end value of the NDSolve. My differential equations and integrating functions are very complex (not related to complex numbers) so I need to use NDSolve and NIntegrate. I was able to get to the point of getting the result of NDSolve. Now I'm unable to get any further. Here is a toy problem which is similar to my big code. 

ClearAll[Evaluate[StringJoin[Context[], "*"]]]
Needs["Utilities`CleanSlate`"]; 
CleanSlate[]; 
ClearInOut[];

c[r_] := E^(-r);

func1[r_, t_] := r + t;

x1x2[r2_, c2_, t2_] := Module[{r = r2, c = c2, t0 = t2}, 
    Reap[
    NDSolve[{Derivative[1][x11][t3] == x11[t3]^2 +c func1[r, t3], 
        WhenEvent[t3 == t0, Sow[x11[t3]]],
         x11[0] == 0},
          {},
           {t3, t0}]][[-1,1,1]]];

x1[r_, t_] := x1x2[r, c[r], t]; 
x1[0, 1/30]

l[r_, t_] := func1[r, t]*x1[r, t]; 

finalF[(t_)?NumericQ] := NIntegrate[l[rr, t], {rr, 0, 1}, MaxRecursion -> 50, 
    AccuracyGoal -> 10, Method -> {"LocalAdaptive", "SymbolicProcessing" -> 0}, 
    PrecisionGoal -> 10];  

finalF[1/30]  

Plot[final[tt],{tt,0,1}]

I used the solution method described in this answer to obtain the final result of NDSolve.

Any one kindly suggest me how to proceed. Thank you

J. M.'s missing motivation
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Gummala Navneeth
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  • If it's any help, you can compute the antiderivative of an NDSolve solution with Integrate. For instance, yFN = y /. First@NDSolve[{y''[x] == x y[x] - y[x]^2, y'[0] == 0, y[0] == 1}, y, {x, 0, 10}]; Integrate[yFN[x], x] – Michael E2 Apr 15 '20 at 12:37
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    What is a role parameter c=c2 plays in a module? – Alex Trounev Apr 15 '20 at 12:54
  • @Alex Trounev, hi, sorry for missing "c" in my code .i have edited my code .Kindly suggest me approach .thank-you – Gummala Navneeth Apr 15 '20 at 13:37
  • @ Michael E2 . Hi thanks for the response .Since my function complex I won't be able to use Integrate function. – Gummala Navneeth Apr 15 '20 at 14:04

1 Answers1

4

Perhaps it's easier to use ParametricNDSolveValue instead of Sow/Reap, because you can require only the last point of the interpolation (evaluated by NDSolve) !

Try 

X11 = ParametricNDSolveValue[{Derivative[1][x11][t3] ==x11[t3]^2 + c[r] func1[r, t3], x11[0] == 0},x11 [t0], {t3, 0, t0}, {r, t0}] 
(* returns x11[t0] !*)

for example

X11[0, 1/30] 
(* 0.000555558 *)

further integration

l[r_, t_] := func1[r, t]*X11[r, t] ;
finalF[ t_ ?NumericQ] := NIntegrate[l[rr, t], {rr, 0, 1}] 
Plot[finalF[tt], {tt, 0, 1}]

enter image description here

Ulrich Neumann
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