Computational Physics, Python, Math, Physics.
2*dt*V_init[i,1:N_y -1]) + Cx2*(q[i,1:N_y -1] + q[i-1,1:N_y -1])*(u_n[i-1,1:N_y -1] - u_n[i,1:N_y -1]) + Cy2*( 0.5*(q[i,1:N_y -1] + q[i,2:N_y])*(u_n[i,2:N_y] - u_n[i,1:N_y -1]) - 0.5*(q[i,0:N_y -2] + q[i,1:N_y -1])*(u_n[i,1:N_y -1] - u_n[i,0:N_y -2]) ) j = N_y u_np1[1:N_x -1,j] = 2*u_n[1:N_x -1,j]