In this work, two semi-analytical methods are introduced in
order to handle the solution of the Fornberg-Whitham equation. The
first one method has been proposed by Temimi and Ansari, namely the
TAM. The second method is the Banach contraction method which is
briefly called the BCM. Both methods do not require using any
additional assumptions. Our calculations are distinguished by an
efficiency and rapidity of obtaining the results, in comparison with the
previous studies for solving the same problem.