Distribution between non-linear branches

[Roger44]

Hello

My question could be about bars and litres/sec but I'll express it as volts and ampères, mathematically it's the same puzzle for me. How do you calculate the currents in circuits when there are devices whose resistances are not linear?
In the following network there are 3 low value linear resistances and two 3rd order polynomial devices whose functions are :

V1 = 0.24 x I1^3 - 0.3 x I1^2) + 0.98 x I1 + 3.72
V2 = 0.07 x I2^3 - 0.02 x I2^2) + 0.16 x I2 + 1.57

No mathematical solution other than a successive approximation approach?

Thanks for your help.

 

[haruspex]

You have two cubic functions f and g, and two constant R and V, and you wish to solve
f(i₁)=g(i₂), f(i₁)+R(i₁+i₂) = V. Yes?
Writing x = i₁,
f(x) = g(V/R-f(x)/R-x)
Expanding that will give a polynomial with powers of 6.