# Question:Solve: High dimensional non-linear system, faster alternatives?

## Question:Solve: High dimensional non-linear system, faster alternatives?

Hi,

I have been solving a system of non-linear ODE's for their steady states. This involves solving the rhs of the ODE's =0.

Hence I have been using "solve" in maple to solve a non-linear system.

Recently I have added more detail to the problem and now I am solving eight equations for eight variables and i've left overnight and maple still didnt find a solution. When sigma1=sigma2=0 below the problem is effectively 5-d and maple breezes through the calculation.

I would be grateful if anyone can suggest alternative commands/options for solve that might speed this up.

Also curious to know readers opinions on whether or not coding this up in non-maple software might be a better option.

Below is the system I am solving,

Cheers, Rod

###########################################################################

# Variables are X, Y1, Y2, Z1, Z2, Y2Z1, Y1Z2, Z

# Constants below are all specified before hand except for "a" and "b"

f1 := a*(X+Y1+Y2+Z1+Z2+Y2Z1+Y1Z2+Z)-q*(X+Y1+Y2+Z1+Z2+Y2Z1+Y1Z2+Z)*(X+Y1+Y2+Z1+Z2+Y2Z1+Y1Z2+Z)-b*X-be1R*X*(Y1+Y1Z2)-be2R*X*(Y2+Y2Z1)+(1-nu1R)*gamma1R*Y1+(1-nu2R)*gamma2R*Y2;

f2 := be1R*X*(Y1+Y1Z2)-be2R*Y1*(Y2+Y2Z1)+be1R*Y2*(Y1+Y1Z2)-(al1+b+gamma1R)*Y1;

f3 := be2R*X*(Y2+Y2Z1)+be2R*Y1*(Y2+Y2Z1)-be1R*Y2*(Y1+Y1Z2)-(al2+b+gamma2R)*Y2;

f4 := nu1R*gamma1R*Y1+(1-nu2R)*gamma2R*Y2Z1-(b+sig1*be2R*(Y2+Y2Z1))*Z1;

f5 := nu2R*gamma2R*Y2+(1-nu1R)*gamma1R*Y1Z2-(b+sig2*be1R*(Y1+Y1Z2))*Z2;

f6 := sig1*be2R*(Y2+Y2Z1)*Z1-(al2+b+gamma2R)*Y2Z1;

f7 := sig2*be1R*(Y1+Y1Z2)*Z2-(al1+b+gamma1R)*Y1Z2;

f8 := nu2R*gamma2R*Y2Z1+nu1R*gamma1R*Y1Z2-b*Z;

sols := solve([f1, f2, f3, f4, f5, f6, f7, f8], [X, Y1, Y2, Z1, Z2, Y2Z1, Y1Z2, Z]):

###########################################################################

﻿