# Problems with DAE solution: “Structural analysis indicates that 1 initial conditions are needed to fix the state of the system…”

I'm trying to solve the following problem:

g = 1/3;
Bic = 1;
Bir = 1;
M = 1;

a[x_, t_, i_] = Cos[m[i][t]*x]
Ni[t_, i_] = Integrate[a[x, t, i]^2, {x, 0, 1}]
f[i_] = Integrate[a[x, t, i], {x, 0, 1}]

Tsi[x_, t_] = Sum[a[x, t, i]*T[i][t]*(1/Ni[t, i]), {i, M}] /. x -> 1
B[Tsi_] = Bic*(Tsi[x, t]^(1/3)) + Bir*(1 + g*Tsi[x, t] + 0.5*g^2*Tsi[x, t]^2)*(1 + 0.5*g*Tsi[x, t])

eq1 = Table[
D[T[i][t], t] +
Sum[((m[i][t])^2*KroneckerDelta[i, j] +
D[m[i][t], t]*(-1/Ni[t, j])*
Integrate[x*a[x, t, i]*Sin[x*m[j][t]], {x, 0, 1}])*
T[j][t], {j, M}] == 0, {i, M}]

eq2 = Table[T[i][0] == 1*f[i] /. t -> 0, {i, M}]

eq3 = Table[-m[i][t]*Sin[m[i][t]] + B[Tsi]*Cos[m[i][t]] == 0, {i, M}]

nsol = NDSolve[{eq1, eq2, eq3}, {Table[T[i], {i, M}],
Table[m[i], {i, M}]}, {t, 0.5}]

The problem is that when I try to solve it with NDSolve appears an error message:

NDSolve::chknic: Structural analysis indicates that 1 initial conditions are needed to fix the state of the system. Currently only 0 initial conditions are specified. NDSolve may return one of a family of solutions.

What does this error means? Because when I try Evaluate[T[1][0.1] /. nsol] I'm not getting any solution.

• "What does this error means? Because when I try Evaluate[T[1][0.1] /. nsol] I'm not getting any solution." There's no causality here, try aaa /. {aaa} -> 1 and think about the reason. – xzczd Jul 14 '19 at 3:34
• There is not enough initial data. Add eq4 = Table[T[i][0] == 1, {i, M}]; and use this code var = Flatten[{Table[T[i], {i, M}], Table[m[i], {i, M}]}]; nsol = NDSolve[{eq1, eq2, eq3, eq4}, var, {t, 0.5}]; {Plot[T[1][t] /. nsol, {t, 0, .5}], Plot[m[1][t] /. nsol, {t, 0, .5}]} – Alex Trounev Jul 14 '19 at 3:53
• Thanks for the help guys – Igor Jul 15 '19 at 18:56