code: def nonlin_bc_bc(ya, yb):
      phiA, phipA = ya
      phiC, phipC = yb
  
      kappa, ioA, ioC, V, f = 1.64, 0.01, 1.0e-4, 0.5, 38.9
  
      # Butler-Volmer Kinetics at Anode
      hA = 0.0 - phiA - 0.0
      iA = ioA * (np.exp(f * hA) - np.exp(-f * hA))
      res0 = iA + kappa * phipA
  
      # Butler-Volmer Kinetics at Cathode
      hC = V - phiC - 1.0
      iC = ioC * (np.exp(f * hC) - np.exp(-f * hC))
      res1 = iC - kappa * phipC
  
      return np.array([res0, res1])
  
imports: import sys
  import numpy
  from numpy.testing import assert_, assert_array_equal, assert_allclose, assert_equal
  from pytest import raises
  from scipy.sparse import coo_matrix
  from scipy.special import erf
  from scipy.integrate._bvp import modify_mesh, estimate_fun_jac, estimate_bc_jac, compute_jac_indices, construct_global_jac, solve_bvp
label_desc: Use image node_id 31 for calling a global function with example usage: nonlin_bc_bc(ya, yb) and returns: np