problem solving nonlinear equation system with fsolve

Hi,

I'm trying to solve the following equation system

P = 1;
lambda = 1;
Maugis = @(X) [lambda*X(1)^2/2*(sqrt(X(3)^2-1)+(X(3)^2-2)*atan(sqrt(X(3)^2-1)))
                +4/3*lambda^2*X(1)*(sqrt(X(3)^2-1)*atan(sqrt(X(3)^2-1))-X(3)+1)-1; 
               X(1)^2-4/3*X(1)*lambda*sqrt(X(3)^2-1)-X(2); 
               X(1)^3-lambda*X(1)^2*(sqrt(X(3)^2-1)+X(3)^2*atan(sqrt(X(3)^2-1)))-P];
X0 = [1;1;1];
sol = fsolve(Maugis,X0);

but did not succeed using fsolve:

Warning: Trust-region-dogleg algorithm of FSOLVE cannot handle non-square systems; using Levenberg-Marquardt algorithm
instead. 
> In fsolve (line 298)
  In solve_equs (line 8) 

No solution found.

fsolve stopped because the last step was ineffective. However, the vector of function
values is not near zero, as measured by the default value of the function tolerance. 

<stopping criteria details>

I'm happy for any help!

Answer 1

[Torsten]

Try

Maugis = @(X) [lambda*X(1)^2/2*(sqrt(X(3)^2-1)+(X(3)^2-2)*atan(sqrt(X(3)^2-1)))+4/3*lambda^2*X(1)*(sqrt(X(3)^2-1)*atan(sqrt(X(3)^2-1))-X(3)+1)-1;... 
               X(1)^2-4/3*X(1)*lambda*sqrt(X(3)^2-1)-X(2);... 
               X(1)^3-lambda*X(1)^2*(sqrt(X(3)^2-1)+X(3)^2*atan(sqrt(X(3)^2-1)))-P];
           

Best wishes

Torsten.

[Peter Uwsen]

Simple solution indeed..

Thanks a lot!

Answer 2

[Alex Sha]

here are solutions:

x1: 1.80929329243556

x2: 1.67586180846898

x3: 1.19942316545143