  Bond propagation and site propagation algorithm are extended to the two
dimensional Ising model with a surface field. With these algorithms we can
calculate the free energy, internal energy, specific heat, magnetization,
correlation function, surface magnetization, surface susceptibility and surface
correlation. To test these algorithms, we study the Ising model for wetting
transition, which is solved exactly by Abraham. We can locate the transition
point accurately to $10^{-8}$. We carry out the calculation of the specific
heat, surface susceptibility on the lattices with the sizes are up to $200^2
\times 200$. The results show that finite jump develops in the specific heat
and surface susceptibility at the transition point as the lattice size
increases. On the lattice with size $320^2 \times 320$ the parallel correlation
length exponent is $1.88$, while in the Abraham's exact result it is $2.0$. The
perpendicular correlation length exponent on the lattice with size $160^2\times
160$ is $1.04$, where its exact value is $1.0$.
