# ERROR: singularity or stiff system suspected (DAE)

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 I have written a code rro = 0.1; c = 3*10^10 ; w1 = 2.126*10^15; k1[\[Tau]] = 59266.66* Sqrt[0.995 +0.00252/(1 - (3*n[\[Tau]]^3)/5)]; k2[\[Tau]] = (118533.3333)* Sqrt[(-0.001255) +0.00252/(1 - (12*n[\[Tau]]^3)/5)]; ko[\[Tau]] = k2[\[Tau]] - 2*k1[\[Tau]]; k01[\[Tau]] = ko[\[Tau]]/k1[\[Tau]]; kcw[\[Tau]] = (k1[\[Tau]]*c)/w1; s1 = NDSolve[{z'[\[Tau]] - (0.4*Exp[-\[Tau]^2]*Exp[-rro^2])/( 10^-5/(z[\[Tau]])^1.5 + (z[\[Tau]])^1.5 (1 - 1.67/ z[\[Tau]]^3)^2) + (2*z[\[Tau]]*n'[\[Tau]])/n[\[Tau]] == 0, n'[\[Tau]] - 0.3*(z[\[Tau]])^0.5 == 0, eta[\[Tau]] - Abs[ 1/(1 -kcw[\[Tau]]^2*(1 + k01[\[Tau]]/2)^2 -0.0012) (kcw[\[Tau]]*((12.59*10^-5)/( n[\[Tau]]^3*3*(1 - 5/(3*n[\[Tau]]^3))^2)) *(( 3*(1 - 5/(6*n[\[Tau]]^3)))/( 8*(1 - 5/(12*n[\[Tau]]^3))^2) +((1 + k01[\[Tau]])/(1 - 5/( 3*n[\[Tau]]^3)))) +kcw[\[Tau]]*0.000138*(1 + 8/11 k01[\[Tau]]))] == 0, z[0] == 1, n[0] == 1}, {z[\[Tau]], n[\[Tau]], eta[\[Tau]]}, {\[Tau], 1}, MaxSteps -> Infinity] t1 = Plot[z[\[Tau]] /. s1, {\[Tau], 0, 1}, PlotStyle -> {Thickness[0.006]}, AxesLabel -> {\[Tau], z}, PlotRange -> {0.00, 20}] t2 = Plot[eta[\[Tau]] /. s1, {\[Tau], 0, 0.6}, PlotStyle -> {Thickness[0.006]}, AxesLabel -> {\[Tau], eta}, PlotRange -> {0, 1}] t3 = Plot[n[\[Tau]] /. s1, {\[Tau], 0, 1}, PlotStyle -> {Thickness[0.006]}, AxesLabel -> {\[Tau], n}, PlotRange -> {0.00, 4}] It is giving an error : at [Tau] == 0.536392, step size is effectively zero; singularity or stiff system suspected. >>Kindly tell me the solution of the problem, How can i get the plot of eta with tau beyond 0.536392 Program file is attached here for reference Attachments: