Solve nonlinear equations within range

Hello,

I have two nonlinear equations to solve simultaneously:

syms x, y
f1 = x^2 + y^2 + x == 4
f2 = x^3 + y*2 == 2

I want to find the solutions (if there's any), when x belongs to the range of [-1,1]. And I don't want to make another matlab file whose purpose is to group the above equations. Because most of the time, the equations are derived from the using symbolic tools earlier in same matlab script and it would be inconvenient to make a separate file.

In this case, what is the way to achieve my goal?

Thanks in advance.

Steph

Answer 1

[Matt J]

syms x  y

assume(x>=-1 & x<=1)

f1 = x^2 + y^2 + x == 4
f2 = x^3 + y*2 == 2
[solx,soly]=vpasolve(f1,f2,x,y)

[Stephen]

Fantastic! Thank you very much.

[madhan ravi]

Are you sure solx and soly return empty values

[Matt J]

Empty values are the correct answer here. The equations have no solution for -1<=x<=+1.

[madhan ravi]

+1 Oh thank you @Matt learnt a new method using vpasolve()

[Stephen]

Following up this thread.

If I would like to use "fsolve" command for these non-linear equations, do I have to define all the functions in a seperate m-file? Can I use "function handle" for the task?

I use fsolve because I want to adjust the stopping criteria for vpasolve. I don't really need it to be as accurate as 10^-12.

[Matt J]

You can't apply bounds with fsolve, but you can with lsqnonlin. Yes, the input is to be a function handle. The function can reside anywhere that a function handle can find it, e.g., it can be a separate mfile, or a nested function, or an anonymous function, or a local function, or a class method, or a class-related function.

[Stephen]

Isn't that function is supposed to be used for curve fitting?

How do I convert those two non-linear equations so that I can use lsqnonlin?

[Matt J]

Example:

fun=@(p) [p(1)^2+p(2)^2+p(1)-4; p(1)^2+2*p(2)-2];

[p,resnorm,~,exitflag]=lsqnonlin(fun,[0,0],[-3,-inf],[+3,+inf])

if resnorm>TOO_BIG
 warning 'The result does not satisfy equations well.'
end