how to get numerical solution to system of non-linear equations?

Any one knows how to get numerical solution to system of non-linear equations?

If vg is varying from 0 to 2 in steps of 0.01, i.e vg=linspace(0,2,N), N=100 n is varying from 1 to N

eq1(n) = (xo2(n) xo(n) xar(n) - 1-Vg(n))=0;
eq2(n) =(2*xo2(n) xo(n) -4*xar(n)-4*Vg(n))=0;
eq3(n) = (2.063E-4*xo2(n) - xo(n)^2)=0;

how to solve roots (xo, xo2, xar) for the above three equations at each value of Vg(0 to 2 in steps of 0.01)?

[Walter Roberson]

Is xo2(n) xo(n) xar(n) expressing implicit multiplication between the terms?

Is xo(n) expressing multiplication or is it expressing array indexing?

Answer 1

[Alan Weiss]

If you have Optimization Toolbox, look into Systems of Nonlinear Equations. You will have to formulate your problem as one of a single vector variable x.

Alan Weiss

MATLAB mathematical toolbox documentation

Answer 2

[Walter Roberson]

If you have the Symbolic Toolbox then assuming that multiplication is being used and that (n) represents indexing, then you can solve() to get exact solutions. A cubic equation is involved, multiplied by a quadratic, so there are (3*2) = 6 solutions. For example one of the solution sets is

xo(n) = (Vg(n) + (Vg(n)^2 + 2*Vg(n)+2)^(1/2)) / ((9452254/975) * Vg(n) * (Vg(n)^2 + 2*Vg(n) + 2)^(1/2) + (9452254/975) * Vg(n)^2 + (9452254/975) *Vg(n) + 9452254/975)^(1/3)
xo2(n) = ((9452254/975) * Vg(n) * (Vg(n)^2 + 2 * Vg(n) + 2)^(1/2) + (9452254/975) * Vg(n)^2 + (9452254/975) * Vg(n) + 9452254/975)^(1/3)
xar(n) = -(1/2) * Vg(n) + (1/2) * (Vg(n)^2 + 2 * Vg(n) + 2)^(1/2)