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I am solving a system consisted of 3 ODEs using ParametricNDSolveValue. Everytime when I want to obtain each solution at certain parameters, I would use:

solutions = ParametricNDSolveValue[{ODEs}, {a, b, phi}, {x, 0, 1}, {TM, miumaxA, miumaxB}];
asol[x_]=solutions[para1val,para2val,para3val][[1]][x];
bsol[x_]=solutions[para1val,para2val,para3val][[2]][x];
phisol[x_]=solutions[para1val,para2val,para3val][[3]][x];

However, this might waste computational resource, as the solution is computed 3 times, in each line. Then, I try :

{asol,bsol,phisol}=solutions[para1val,para2val,para3val][x];

However, this does not work. solutions[para1val,para2val,para3val][x] would give a list of three interpolating functions. Is there any way to extract interpolating function of each solution once solutions[para1val,para2val,para3val][x] is evaluated?

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  • $\begingroup$ It would be better to provide code that is self-contained. As it stands, everyone has to invent their own ode to run your code. In any event, try dropping [x] and write {asol,bsol,phisol} = solutions[para1val,para2val,para3val] instead, does that do it? For example, try evaluating asol[0.5] afterwards. $\endgroup$
    – user293787
    Commented Jul 9, 2022 at 11:07
  • $\begingroup$ Try to write asol[x_]:=solutions... instead of asol[x_]=solutions.... You may also define sol[x_, n_Integer]:=solutions[para1val,para2val,para3val][[n]][x], which yields you the solution definition for all values n=1,2,3. In principle, this makes what you want: the function definition persisting through the whole Mma session. $\endgroup$
    – Alexei Boulbitch
    Commented Jul 9, 2022 at 12:31
  • $\begingroup$ @user293787 The complete code is available in the link provided in the question. $\endgroup$
    – Johnson
    Commented Jul 9, 2022 at 12:53
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    $\begingroup$ @user293787 By dropping [x] , I am able to get asol[x], bsol[x], and phisol[x] as separated interpolating function. Your help is very much appreciated. @AlexeiBoulbitch By changing to :=, I would get error message "dSetDelayed::shape". $\endgroup$
    – Johnson
    Commented Jul 9, 2022 at 13:09
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    $\begingroup$ ParametricNDSolveValue caches results by default, so the ODEs won't be repeatedly solved and re-solved. It was designed with your sort of use-case in mind. $\endgroup$
    – Michael E2
    Commented Jul 9, 2022 at 17:07

1 Answer 1

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Turning the comment to an answer:

ParametricNDSolveValue caches results by default, so the ODEs won't be repeatedly solved and re-solved. It was designed with your sort of use-case in mind.

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