code: def implicit_step():
      """Creates a stepper function with implicit time marching scheme.
  
      Given a space-discretized equation
  
      ```
      du/dt = A(t) u(t) + b(t)
      ```
      (here `u` is a value vector, `A` and `b` are the matrix and the vector defined
      by the PDE), the implicit time marching scheme approximates the right-hand
      side with its value after the time step:
  
      ```
      (u(t2) - u(t1)) / (t2 - t1) = A(t2) u(t2) + b(t2)
      ```
      This scheme is stable, but is only first order accurate.
      Usually, Crank-Nicolson or Extrapolation schemes are preferable.
  
      More details can be found in `weighted_implicit_explicit.py` describing the
      weighted implicit-explicit scheme - implicit scheme is a special case
      with `theta = 0`.
  
      Returns:
        Callable to be used in finite-difference PDE solvers (see fd_solvers.py).
      """
  
      def step_fn(
          time,
          next_time,
          coord_grid,
          value_grid,
          boundary_conditions,
          second_order_coeff_fn,
          first_order_coeff_fn,
          zeroth_order_coeff_fn,
          inner_second_order_coeff_fn,
          inner_first_order_coeff_fn,
          num_steps_performed,
          dtype=None,
          name=None,
      ):
          """Performs the step."""
          del num_steps_performed
          name = name or "implicit_step"
          return parabolic_equation_step(
              time,
              next_time,
              coord_grid,
              value_grid,
              boundary_conditions,
              second_order_coeff_fn,
              first_order_coeff_fn,
              zeroth_order_coeff_fn,
              inner_second_order_coeff_fn,
              inner_first_order_coeff_fn,
              time_marching_scheme=implicit_scheme,
              dtype=dtype,
              name=name,
          )
  
      return step_fn
  
label_desc: Use image node_id 1 for calling a global function with example usage: implicit_step() and returns: step_fn, parabolic_equation_step