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I am trying to solve a set of coupled differential eqns., but getting the errors as mentioned in the title.

replace = 
  {Subscript[m, ϕ] -> 10^-5, Γ -> 10^-11, λ -> 0.01, ξ -> -1, m -> 10^-21,  
   k -> 10^59, Subscript[M, P] -> 1};

V[t_] := 1/2 Subscript[m, ϕ]^2  ϕ[t]^2  /. replace ;


R[t_] := Subscript[M, P]^-2 (4 V[t] - ϕ'[t]^2/(k^2 a[t]^2)) /. replace;


χi[t_] := ((- ξ R[t] - m^2)/λ)^(1/2) /. replace;


eqna = 
   ϕ''[t] + 2 a'[t]/a[t] ϕ'[t] + k a[t] Γ ϕ'[t] + k^2 a[t]^2 D[V[t], ϕ[t]] /. replace;


eqnb = 
  χ''[t] + 2 a'[t]/a[t] χ'[t] + k^2 a[t]^2 λ χ[t]^3 + k^2 a[t]^2 m^2 χ[t] + 
  k^2 a[t]^2 ξ R[t] χ[t] /. replace;


eqnc = 
  k  Subscript[ρ, r]'[t]/a[t] + 4 k  a'[t]/a[t]^2 Subscript[ρ, r][t] - 
  Γ ϕ'[t]^2/a[t]^2 /. replace;


eqnd = 
  a'[t]/a[t] -
    Sqrt[
      1/(3 Subscript[M, P]^2) 
        (1/2 ϕ'[t]^2 + k^2 a[t]^2 V[t] + k^2 a[t]^2 Subscript[ρ, r][t])]
/. replace;


sol1 = 
  NDSolve[
    {eqna == 0 , eqnb == 0, eqnc == 0, eqnd == 0,  ϕ[-60 ] == 15 , 
     ϕ'[-60] == 0, χ[-60] == χi[-60], χ'[-60] == 0, 
     Subscript[ρ, r][-60] == 10^-20, a[-60] == Exp[-70]}, 
    {ϕ, χ, Subscript[ρ, r], a}, {t, -60, 5}] // FullSimplify

Error:NDSolve::ndsz: At t == -60., step size is effectively zero; singularity or stiff system suspected.

I think other solutions to this problem ndsz : step size is effectively zero; singularity or stiff system suspected didn't match with my problem.

Also, while plotting: Plot[{Evaluate[Abs[χ[t]] /. sol1]}, {t, -60, 5}, PlotRange -> All, ImageSize -> Large, Frame -> True] error is appearing as : InterpolatingFunction::dmval: Input value {-59.9987} lies outside the range of data in the interpolating function. Extrapolation will be used.

Note that -59.9 is inside the range.

surujjd
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  • Regarding the second error: notice that the results from NDSolve are interpolating functions with a domain $[-60, -60]$, i.e. the integration did not proceed at all, and the only value available is -60. Is your system stiff? Do you have a singularity at t=-60? This is a pretty common problem: what have you tried specifically (with code) and what was the result? – MarcoB Jun 19 '20 at 21:01
  • Oh I see. But I got the plot(may be through extrapolation), though not the correct one as expected. I don't see any singularity at t=-60. I was trying to solve a physics problem: evolution of some quantities such as scale factor of the Universe, some quantum fields etc. with time(conformal time). I didn't get the result as required. Earlier I was trying to do the same problem in a different variable(physical time), but I think computation was too heavy there large range. – surujjd Jun 20 '20 at 08:51
  • @surujjd Let check coefficients of your system: there are $10^{108}$ in eqna , $10^{118}$ in eqnb and eqnd. How we can handle this with numerical methods? – Alex Trounev Jun 20 '20 at 10:47

0 Answers0