parameters: (a, u, freedofs=None, maxit=100, maxerr=1e-11, inverse="umfpack", \
                 dirichletvalues=None, dampfactor=1, printing=True, callback=None)
return_statement: return solver.Solve(maxit=maxit, maxerr=maxerr,
                          dampfactor=dampfactor,
                          printing=printing,
                          callback=callback,
                          linesearch=False,
                          printenergy=False)
docstring: Newton's method for solving non-linear problems of the form A(u)=0.
  
      Parameters
      ----------
      a : BilinearForm
        The BilinearForm of the non-linear variational problem. It does not have to be assembled.
  
      u : GridFunction
        The GridFunction where the solution is saved. The values are used as initial guess for Newton's method.
  
      freedofs : BitArray
        The FreeDofs on which the assembled matrix is inverted. If argument is 'None' then the FreeDofs of the underlying FESpace is used.
  
      maxit : int
        Number of maximal iteration for Newton. If the maximal number is reached before the maximal error Newton might no converge and a warning is displayed.
  
      maxerr : float
        The maximal error which Newton should reach before it stops. The error is computed by the square root of the inner product of the residuum and the correction.
  
      inverse : string
        A string of the sparse direct solver which should be solved for inverting the assembled Newton matrix.
  
      dampfactor : float
        Set the damping factor for Newton's method. If dampfactor is 1 then no damping is done. If value is < 1 then the damping is done by the formula 'min(1,dampfactor*numit)' for the correction, where 'numit' denotes the Newton iteration.
  
      printing : bool
        Set if Newton's method should print informations about the actual iteration like the error. 
  
      Returns
      -------
      (int, int)
        List of two integers. The first one is 0 if Newton's method did converge, -1 otherwise. The second one gives the number of Newton iterations needed.
docstring_summary: Newton's method for solving non-linear problems of the form A(u)=0.
docstring_tokens: Newton s method for solving non - linear problems of the form A ( u ) = 0 .
function: def Newton(a, u, freedofs=None, maxit=100, maxerr=1e-11, inverse="umfpack", \
                 dirichletvalues=None, dampfactor=1, printing=True, callback=None):
      """
      Newton's method for solving non-linear problems of the form A(u)=0.
  
      Parameters
      ----------
      a : BilinearForm
        The BilinearForm of the non-linear variational problem. It does not have to be assembled.
  
      u : GridFunction
        The GridFunction where the solution is saved. The values are used as initial guess for Newton's method.
  
      freedofs : BitArray
        The FreeDofs on which the assembled matrix is inverted. If argument is 'None' then the FreeDofs of the underlying FESpace is used.
  
      maxit : int
        Number of maximal iteration for Newton. If the maximal number is reached before the maximal error Newton might no converge and a warning is displayed.
  
      maxerr : float
        The maximal error which Newton should reach before it stops. The error is computed by the square root of the inner product of the residuum and the correction.
  
      inverse : string
        A string of the sparse direct solver which should be solved for inverting the assembled Newton matrix.
  
      dampfactor : float
        Set the damping factor for Newton's method. If dampfactor is 1 then no damping is done. If value is < 1 then the damping is done by the formula 'min(1,dampfactor*numit)' for the correction, where 'numit' denotes the Newton iteration.
  
      printing : bool
        Set if Newton's method should print informations about the actual iteration like the error. 
  
      Returns
      -------
      (int, int)
        List of two integers. The first one is 0 if Newton's method did converge, -1 otherwise. The second one gives the number of Newton iterations needed.
  
      """
      solver = NewtonSolver(a=a, u=u, freedofs=freedofs, inverse=inverse)
      if dirichletvalues is not None:
          solver.SetDirichlet(dirichletvalues)
      return solver.Solve(maxit=maxit, maxerr=maxerr,
                          dampfactor=dampfactor,
                          printing=printing,
                          callback=callback,
                          linesearch=False,
                          printenergy=False)
function_tokens: def Newton ( a , u , freedofs = None , maxit = 100 , maxerr = 1e-11 , inverse = "umfpack" , dirichletvalues = None , dampfactor = 1 , printing = True , callback = None ) : solver = NewtonSolver ( a = a , u = u , freedofs = freedofs , inverse = inverse ) if dirichletvalues is not None : solver . SetDirichlet ( dirichletvalues ) return solver . Solve ( maxit = maxit , maxerr = maxerr , dampfactor = dampfactor , printing = printing , callback = callback , linesearch = False , printenergy = False )