I am trying to solve four coupled nonlinear differential equations.

But, everytime I am getting

NDSolve::ndsz: At t == 2.0833315360868916`, step size is effectively zero; singularity or stiff system suspected.

I have tried all the possible ways to solve such kind of problem with similar kind of problems available in stack.

I want to get the value of g1,g2,g3 and g4 for large value of t i.e. 1 to 100 but I am getting only for small value of t?

Could you please suggest me some way to sort out the issue?

(Eta) = 0.125;

rg1s = Derivative(1)(u1)(t) – u1(t)*u3(t) – 3*u1(t)*u4(t) + u2(t) u3(t) + 3u2(t)u4(t) + 2(1 + 2*(Eta))

*u1(t)^2 == 0;*

rg2s = Derivative(1)(u2)(t) – u2(t)u4(t)^2 + 6

rg2s = Derivative(1)(u2)(t) – u2(t)

*u3(t) – 3*u2(t)*u4(t) + u1(t)*(Eta))*u3(t) + 3*u1(t)*u4(t) + 2*(1 + 2*u2(t)^2 == 0;*

rg3t = Derivative(1)(u3)(t) – 0.5((u1(t) – u2(t))^2 + u3(t)^2 – 3rg3t = Derivative(1)(u3)(t) – 0.5

*u3(t)*u4(t)^2 – 2

*u4(t)) == 0;*

rg4t = Derivative(1)(u4)(t) – 0.5((u1(t) – u2(t))^2 + u3(t)^2 + 5rg4t = Derivative(1)(u4)(t) – 0.5

*u3(t)*0.2, u3(0) == 0.6*0.2, u4(0) == 0.2}, {u1, u2, u3, u4}, {t, 1, 10})

*u4(t)) == 0;*

sol = NDSolve({rg1s, rg2s, rg3t, rg4t, u1(0) == -0.60.2, u2(0) == -0.6sol = NDSolve({rg1s, rg2s, rg3t, rg4t, u1(0) == -0.6

Thank you