Questions about nonlinear problem with mixed boundary condition

General Discussion
1

Hello all users

I have a question about making a FreeFEM code for my problem. To be specific, as a simple nonlinear problem, I tried to solve the following differential equations.

F’‘(x) + F(x) - F(x)^3 =0, F(0) =0, F’(\infty) = 0

So, the solution for the above differential equation is tanh(x/\sqrt(2)).

In order to solve this nonlinear equation, I follow some examples in official documents.

The below codes are my code;

func InitialCondition = 1. * (x>0) + 0.;
mesh Th = square(100, 10, [10 *x, 2 * y]);
fespace Vh(Th, P2  , periodic = [[1,x], [3,x] ]  );
Vh u, v;
Vh du;
Vh uold = InitialCondition;

for(int i = 1; i < 7; i++){
solve example(du,v)
  =   int2d(Th)(  ( dx(du  ) * dx(v) + dy(du)   * dy(v) )  - du   * v + 3 * ( dx(du))* uold * uold * v )
    - int2d(Th)(  ( dx(uold) * dx(v) + dy(uold) * dy(v) )  - uold * v +   uold * uold * uold * v)
    + on( 4, du = 0);
    uold[] -= du[];

    plot(uold );
}

Whenever I modified this code, I couldn’t reach to correct solutions.

Thank you for your help