# Issue with Manipulate (in order to fit) of complicated Parametric NDSolve

So I have a quite complicated ParametricNDSolve :

taustart=5;
epsilon=0.0001;
v=600;
L=1000;
D0=9*10^4;
nR=1;

sol = ParametricNDSolve[
{R'[
t] ==  (D0 E^(-((L - t v)^2/(4 D0 t))) (L + t v))/(
4 Sqrt[\[Pi]] (D0 t)^(
3/2))*(phi0*R0^3*4*Pi/3)/phi0/(4 Pi*R[t]^2) + ((-16 R[t]^3 + (
32 alpha E^(-((3 Vphi[t])/(4 phil \[Pi] R[t]^3)))
l0 nR R[
t]^4 (-2 l0 \[Pi] + (
Sqrt[3 \[Pi]]
Coth[(Sqrt[3/\[Pi]] R[t])/(
2 l0 Sqrt[(
E^(-((3 Vphi[t])/(4 phil \[Pi] R[t]^3))) R[t]^3)/
Vphi[t]])] R[t])/Sqrt[(
E^(-((3 Vphi[t])/(4 phil \[Pi] R[t]^3))) R[t]^3)/Vphi[t]]))/
Vphi[t] - (6 beta Vphi[t])/\[Pi] + (
3 beta Vphi[
t] (-2 interface^2 \[Pi]^2 R[t] +
24 interface Log[2] R[t]^2 - 8 R[t]^3 +
3 interface^3 (4 PolyLog[3, -E^(-((2 R[t])/interface))] +
3 Zeta[3])))/(4 \[Pi] R[t]^3))/(48 taug R[t]^2)) +
Rcomp[R[t], R0]*If[t < taustartc, 0.001, 1],
R[epsilon] == epsilon,

Vphi'[t] == (D0 E^(-((L - t v)^2/(4 D0 t))) (L + t v))/(
4 Sqrt[\[Pi]] (D0 t)^(
3/2))*(phi0*R0^3*4*Pi/3) + ((-16 R[t]^3 + (
32 alpha E^(-((3 Vphi[t])/(4 phil \[Pi] R[t]^3)))
l0 nR R[t]^4 (-2 l0 \[Pi] + (
Sqrt[3 \[Pi]]
Coth[(Sqrt[3/\[Pi]] R[t])/(
2 l0 Sqrt[(
E^(-((3 Vphi[t])/(4 phil \[Pi] R[t]^3))) R[t]^3)/
Vphi[t]])] R[t])/Sqrt[(
E^(-((3 Vphi[t])/(4 phil \[Pi] R[t]^3))) R[t]^3)/
Vphi[t]]))/Vphi[t] - (6 beta Vphi[t])/\[Pi] + (
3 beta Vphi[
t] (-2 interface^2 \[Pi]^2 R[t] +
24 interface Log[2] R[t]^2 - 8 R[t]^3 +
3 interface^3 (4 PolyLog[3, -E^(-((2 R[t])/interface))] +
3 Zeta[3])))/(4 \[Pi] R[t]^3))/(
48 taug R[t]^2))*1/((4 \[Pi] R[t]^3)/(3*Vphi[t]))*4*Pi*R[t]^2,
Vphi[epsilon] == 4*Pi/3*epsilon^3*phi0},

{R, Vphi}, {t, epsilon,
200}, {R0, alpha, beta, tauc, taug, l0, phil, interface}]


I want to fit it to :

rad={{0., 117.705}, {3., 148.255}, {6., 176.81}, {9., 183.561}, {12.,
197.419}, {15., 210.672}, {18., 211.152}, {21., 209.889}, {24.,
207.741}, {27., 204.352}, {30., 201.79}, {33., 199.976}, {36.,
199.04}, {39., 197.151}, {42., 197.584}, {45., 196.198}, {48.,
195.153}, {51., 195.711}, {54., 194.088}, {57., 193.304}, {60.,
192.474}, {63., 192.13}, {66., 192.877}, {69., 192.371}, {72.,
192.657}, {75., 190.984}, {78., 190.685}, {81., 190.449}, {84.,
189.83}, {87., 189.625}, {90., 194.855}, {93., 186.581}, {96.,
184.735}, {99., 184.586}, {102., 183.505}, {105., 181.531}, {108.,
179.925}, {111., 178.428}, {114., 176.164}, {117., 175.375}, {120.,
174.782}, {123., 172.649}, {126., 170.454}, {129., 168.357}, {132.,
168.04}, {135., 167.26}, {138., 165.657}, {141., 164.797}, {144.,
163.705}, {147., 161.214}, {150., 160.5}, {153., 159.353}, {156.,
157.873}, {159., 157.225}}


So I'm writting :

Manipulate[
Show[{Plot[(Evaluate@({(R[160, alpha, beta, tauc,
taug, l0, phil, 4] /. sol)[t]})), {t, epsilon, 160},
PlotRange -> All, ImageSize -> Large],
ImageSize -> Large]}],  {{alpha, 10}, 4, 15,
Appearance -> "Labeled"}, {{beta, 0.6}, 0.1, 3,
Appearance -> "Labeled"}, {{tauc, 16}, 2, 30,
Appearance -> "Labeled"}, {{taug, 130}, 50, 200,
Appearance -> "Labeled"}, {{l0, 230}, 100, 300,
Appearance -> "Labeled"}, {{phil, 0.046}, 0.03, 0.06,
Appearance -> "Labeled"}]


which is a not so far to start manipulate.

But if I change the parameters a little bit it starts to be very weird :

I checked my equation and it seems to be right. But it is possible that sometimes parametricNDSolve gives strange results like that ?

• I think the function Rcomp is missing from your question as well as the numerical value of phi0. – Jack LaVigne Jul 26 at 15:14