I have this equation :

eqkk = 
  D[k[t], {t,2}] - ((3 sola'[t]/sola[t]) + (3 sola''[t]/sola'[t]) - 
    (1/(sola'[t] sola[t]^2))) D[k[t], t]

To get $k(t)$:

solk = NDSolveValue[{eqkk == 0, k[0] == 1, k'[0] ==0}, k, {t, tmin,tmax}]`

Now I want to evaluate solk, not at k'[0] == 0, but to take the limit of solk as k'[0] -> 0


sola[t] is another function solved before with NDSolveValue as well. Consider for instance sola[t] is like y[t]

Any help appreciated.

  • $\begingroup$ What's sola[t]? $\endgroup$ – Chris K May 18 at 9:11
  • $\begingroup$ I edit the question. $\endgroup$ – Dr. phy May 18 at 9:20
  • $\begingroup$ It might be easier for people to help you if you provide the code that defines sola[t]. $\endgroup$ – Chris K May 18 at 9:30
  • 1
    $\begingroup$ Wouldn't it be easier to solve the system of ode's in {k[t],sola[t]} in one step? $\endgroup$ – Ulrich Neumann May 18 at 10:10
  • $\begingroup$ @Dr.phy Use solk = ParametricNDSolveValue[{eqkk == 0, k[0] == 1, k'[0] == p}, k, {t, tmin, tmax}, {p}], then the function solk[p][t] has a limit solk[0][t]. $\endgroup$ – Alex Trounev May 18 at 11:26

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