  We have applied the variational $R$-matrix method to calculate the reflection
and tunneling probabilities of particles tunneling through one-dimensional
potential barriers for five different types of potential profiles -- truncated
linear step, truncated exponential step, truncated parabolic, bell-shaped, and
Eckart. Our variational results for the transmission and reflection
coefficients are compared with exact analytical results and results obtained
from other numerical methods. We find that our results are in good agreement
with them. We conclude that the variational $R$-matrix method is a simple,
non-iterative, and effective method to solve one-dimensional quantum tunneling
problems.
