Duffing equation for spring model y"+y+ay^3=0 and can we find x(t),t=10^10? by using RK4 for 1 period (dont forget it is spring model) and in all period spring moves samely and can we find for t=10^10 by using modular aritmetic?
I don't know about the general case, but this example works fine:
eq = y''[t] + y[t] + 2 y[t]^3 == 0; sol = DSolveValue[{eq, y[0] == 0, y'[0] == 1}, y, t] sol[10^10] N[%, 20]
