# problem solving nonlinear equation system with fsolve

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Peter Uwsen on 4 Mar 2019
Answered: Alex Sha on 22 Apr 2019
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
> 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!

Torsten on 4 Mar 2019
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 on 4 Mar 2019
Simple solution indeed..
Thanks a lot!

Alex Sha on 22 Apr 2019
here are solutions:
x1: 1.80929329243556
x2: 1.67586180846898
x3: 1.19942316545143